Ch8 | Test Bank + Answers – Conics And Systems Of Nonlinear - Test Bank | College Algebra 5e by Young by Cynthia Y. Young. DOCX document preview.

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Ch8 | Test Bank + Answers – Conics And Systems Of Nonlinear

College Algebra, 5e (Young)

Chapter 8 Conics and Systems of Nonlinear Equations and Inequalities

8.4 The Hyperbola

1) Find the standard form of the equation of the hyperbola with foci (-7, 0) and (7, 0), and vertices (-6, 0) and (6, 0).

A) ((x) with superscript (2)/36) - ((y) with superscript (2)/13) = 1

B) ((x) with superscript (2)/13) - ((y) with superscript (2)/36) = 1

C) ((y) with superscript (2)/36) - ((x) with superscript (2)/13) = 1

D) ((y) with superscript (2)/13) - ((x) with superscript (2)/36) = 1

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the origin.

2) Find the standard form of the equation of the hyperbola with foci (0, 3) and (0, -3), and vertices (0, 2) and (0, - 2).

A) ((x) with superscript (2)/5) - ((y) with superscript (2)/4) = 1

B) ((x) with superscript (2)/4) - ((y) with superscript (2)/5) = 1

C) ((y) with superscript (2)/4) - ((x) with superscript (2)/5) = 1

D) ((y) with superscript (2)/5) - ((x) with superscript (2)/4) = 1

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the origin.

3) Find the standard form of the equation of the hyperbola with foci (-10, 0) and (10, 0), and vertices (-2, 0) and (2, 0).

A) ((y) with superscript (2)/4) - ((x) with superscript (2)/96) = 1

B) ((x) with superscript (2)/4) - ((y) with superscript (2)/96) = 1

C) ((x) with superscript (2)/96) - ((y) with superscript (2)/4) = 1

D) ((y) with superscript (2)/96) - ((x) with superscript (2)/4) = 1

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the origin.

4) Find the standard form of the equation of the hyperbola with foci (0, -9) and (0, 9), and vertices (0, 2) and (0, -2).

A) ((y) with superscript (2)/77) - ((x) with superscript (2)/4) = 1

B) ((x) with superscript (2)/77) - ((y) with superscript (2)/4) = 1

C) ((x) with superscript (2)/4) - ((y) with superscript (2)/77) = 1

D) ((y) with superscript (2)/4) - ((x) with superscript (2)/77) = 1

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the origin.

5) Find the standard form of the equation of a hyperbola with center (0, 0), transverse x-axis, and asymptotes y = 11x and y = -11x.

A) ((y) with superscript (2)/1) - ((x) with superscript (2)/121) = 1

B) ((x) with superscript (2)/121) - ((y) with superscript (2)/1)= 1

C) ((x) with superscript (2)/1) - ((y) with superscript (2)/121) = 1

D) ((y) with superscript (2)/121) - ((x) with superscript (2)/1)= 1

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the origin.

6) Find the standard form of the equation of a hyperbola with center (0, 0), transverse y-axis, and asymptotes y = -12x and y = 12x.

A) ((x) with superscript (2)/1) - ((y) with superscript (2)/144) = 1

B) ((y) with superscript (2)/144) - ((x) with superscript (2)/1)= 1

C) ((x) with superscript (2)/144) - ((y) with superscript (2)/1)= 1

D) ((y) with superscript (2)/1) - ((x) with superscript (2)/144) = 1

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the origin.

7) Find the standard form of the equation of a hyperbola with center (0, 0), transverse x-axis, and asymptotes y = (3/8)x and y = - (3/8)x.

A) ((x) with superscript (2)/64) - ((y) with superscript (2)/9) = 1

B) ((x) with superscript (2)/9) - ((y) with superscript (2)/64) = 1

C) ((y) with superscript (2)/64) - ((x) with superscript (2)/9) = 1

D) ((y) with superscript (2)/9) - ((x) with superscript (2)/64) = 1

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the origin.

8) Find the standard form of the equation of a hyperbola with center (0, 0), transverse y-axis, and asymptotes y = (7/8)x and y = - (7/8)x.

A) ((y) with superscript (2)/49) - ((x) with superscript (2)/64) = 1

B) ((x) with superscript (2)/64) - ((y) with superscript (2)/49) = 1

C) ((x) with superscript (2)/49) - ((y) with superscript (2)/64) = 1

D) ((y) with superscript (2)/64) - ((x) with superscript (2)/49) = 1

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the origin.

9) Find the standard form of the hyperbola with the following equation.

4(x) with superscript (2) - 6(y) with superscript (2) - 8x - 24y = 44

A) (((x - 1)) with superscript (2)/16) - ((( y + 2)) with superscript (2)/36) = 1

B) (((x + 1)) with superscript (2)/6) - ((( y - 2)) with superscript (2)/4) = 1

C) (((x - 1)) with superscript (2)/6) - ((( y + 2)) with superscript (2)/4) = 1

D) (((x + 1)) with superscript (2)/36) - ((( y - 2)) with superscript (2)/16) = 1

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the point (h, k).

10) Find the standard form of the hyperbola with the following equation.

2(y) with superscript (2) - 3(x) with superscript (2) - 20x - 48y = 148

A) ((( y - 5)) with superscript (2)/3) - (((x + 8)) with superscript (2)/2) = 1

B) ((3(x - 5)) with superscript (2)/3) - ((2( y + 8)) with superscript (2)/2) = 1

C) (((x - 5)) with superscript (2)/290) - ((( y + 8)) with superscript (2)/290) = 1

D) ((2(y - 5)) with superscript (2)/290) - ((3(x + 8)) with superscript (2)/290) = 1

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the point (h, k).

11) Find the standard form of the equation of a hyperbola with foci (0, 10) and (0, -10), and vertices (0, 2) and (0, -2).

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the origin.

12) Find the standard form of the hyperbola with the following equation.

25(x) with superscript (2) - 4(y) with superscript (2) - 50x + 40y - 175 = 0

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the point (h, k).

13) Graph the hyperbola.

An equation reads, x squared minus start fraction y squared over 4 end fraction equals 1.

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 3 to 3, in increments of 0.5. The y axis ranges from negative 3 to 3, in increments of 0.5. The hyperbola is centered at the origin and has two branches. One branch opens leftward with vertex at (negative 1, 0) and passes through the points (negative 1.5, 2.5) and (negative 1.5, negative 2.5). Another branch opens rightward with vertex at (1, 0) and passes through the points (1.5, 2.5) and (1.5, negative 2.5). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Graph a hyperbola using asymptotes as graphing aids.

14) Find the equation of the hyperbola from the given graph.

A vertical hyperbola and two asymptotes are graphed on an x y coordinate plane. The x axis ranges from negative 5 to 5, in increments of 0.5. The y axis ranges from negative 5 to 5, in increments of 0.5. The hyperbola is centered at the origin and has two branches. One branch opens upward with vertex at (0, 2) and passes through the points (negative 4, 4.5) and (4, 4.5). Another branch opens downward with vertex at (0, negative 2) and passes through the points (negative 4, negative 4.5) and (4, negative 4.5). The first asymptote is an upward sloping dashed line that passes through (negative 3, negative 3), (0, 0), and (3, 3). The second asymptote is a downward sloping dashed line that passes through (negative 3, 3), (0, 0), and (3, negative 3) All values are estimated.

An equation reads, y squared minus x squared equals 4.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Graph a hyperbola using asymptotes as graphing aids.

15) Graph the hyperbola.

An equation reads, start fraction x squared over 25 end fraction minus start fraction y squared over 9 end fraction equals 1.

A)

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 10, in increments of 2. The y axis ranges from negative 5 to 5, in increments of 0.5. The hyperbola is centered at the origin and has two branches. One branch opens leftward with vertex at (negative 5, 0) and passes through the points (negative 8, 3.5) and (negative 8, negative 3.5). Another branch opens rightward with vertex at (5, 0) and passes through the points (8, 3.5) and (8, negative 3.5). All values are estimated.

B)

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 6, in increments of 1. The y axis ranges from negative 4 to 4, in increments of 0.5. The hyperbola is centered at the origin and has two branches. One branch opens leftward with vertex at (negative 2, 0) and passes through the points (negative 4, 1.5) and (negative 4, negative 1.5). Another branch opens rightward with vertex at (2, 0) and passes through the points (4, 1.5) and (4, negative 1.5). All values are estimated.

C)

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 8, in increments of 1. The y axis ranges from negative 4 to 4, in increments of 0.5. The hyperbola is centered at the origin and has two branches. One branch opens leftward with vertex at (negative 3, 0) and passes through the points (negative 5, 3) and (negative 5, negative 3). Another branch opens rightward with vertex at (3, 0) and passes through the points (5, 3) and (5, negative 3). All values are estimated.

D)

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 8, in increments of 1. The y axis ranges from negative 4 to 4, in increments of 0.5. The hyperbola is centered at the origin and has two branches. One branch opens leftward with vertex at (negative 4, 0) and passes through the points (negative 6, 2.5) and (negative 6, negative 2.5). Another branch opens rightward with vertex at (4, 0) and passes through the points (6, 2.5) and (6, negative 2.5). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Graph a hyperbola using asymptotes as graphing aids.

16) Find the equation of the hyperbola from the given graph.

A vertical hyperbola and two asymptotes are graphed on an x y coordinate plane. The x axis ranges from negative 6 to 6 in increments of 1. The y axis ranges from negative 6 to 6 in increments of 1. The hyperbola is centered at the origin and has two branches. One branch opens upward with vertex at (0, 3) and passes through the points (negative 4, 5) and (4, 5). Another branch opens downward with vertex at (0, negative 3) and passes through the points (negative 4, negative 5) and (4, negative 5). The first asymptote is an upward sloping dashed line that passes through (negative 4, negative 4), (0, 0), and (4, 4). The second asymptote is a downward sloping dashed line that passes through (negative 4, 4), (0, 0), and (4, negative 4).

A)

An equation reads, y squared minus x squared equals 9.

B)

An equation reads, y squared minus x squared equals 16.

C)

An equation reads, y squared minus x squared equals 25.

D)

An equation reads, y squared minus x squared equals 4.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Graph a hyperbola using asymptotes as graphing aids.

17) Graph the hyperbola.

An equation reads, left parenthesis x minus 1 right parenthesis squared minus start fraction left parenthesis y minus 1 right parenthesis squared over 9 end fraction equals 1.

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 2 to 4, in increments of 0.5. The y axis ranges from negative 4 to 5, in increments of 0.5. The hyperbola has two branches. One branch opens leftward and passes through the points (negative 0.5, 4.5), (0,1), and (negative 0.5, negative 2). Another branch opens rightward and passes through the points (2.5, 4.5), (2, 0), and (2.5, negative 3). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find a hyperbola's foci and vertices.

18) Graph the hyperbola.

An equation reads, left parenthesis x minus 1 right parenthesis squared minus 9 left parenthesis y minus 1 right parenthesis squared equals 9.

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 10, in increments of 1. The y axis ranges from negative 3 to 4, in increments of 0.5. The hyperbola has two branches. One branch opens leftward and passes through the points (negative 5, 3), (negative 2, 1), and (negative 6, negative 1). Another branch opens rightward and passes through the points (7, 3), (4, 1), and (8, negative 1). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find a hyperbola's foci and vertices.

19) Graph the hyperbola.

An equation reads, 4 x squared plus 9 y squared plus 24 x minus 36 y plus 36 equals 0.

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 5, in increments of 1. The y axis ranges from negative 4 to 8, in increments of 1. The hyperbola has two branches. One branch opens leftward and passes through the points (negative 8, 5), (negative 6, 2), and (negative 9, negative 1). Another branch opens rightward and passes through the points (4, 6), (0, 2), and (3, negative 1). All values are estimated.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find a hyperbola's foci and vertices.

20) Find the standard form of the equation of the hyperbola from the given graph.

A vertical hyperbola and two asymptotes are graphed on an x y coordinate plane. The x axis ranges from negative 8 to 10, in increments of 1. The y axis ranges from negative 4 to 2, in increments of 0.5. The hyperbola has two branches. One branch opens upward with vertex at (2, 0) and passes through the points (negative 4, 1) and (6, 1). Another branch opens downward with vertex at (1, negative 2) and passes through the points (negative 5, negative 3.5) and (6, negative 3). The first asymptote is an upward sloping dashed line that passes through (negative 4, negative 2.5), (1, negative 1) and (4, 0). The second asymptote is a downward sloping dashed line that passes through (negative 2, 0), (1, negative 1) and (4, negative 2). All values are estimated.

An equation reads, left parenthesis y plus 1 right parenthesis squared minus start fraction left parenthesis x minus 1 right parenthesis squared over 9 end fraction equals 1.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Graph a hyperbola using asymptotes as graphing aids.

21) Find the equation of the hyperbola from the given graph.

A vertical hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 10, in increments of 1. The y axis ranges from negative 5 to 3, in increments of 0.5. The hyperbola has two branches. One branch opens upward with vertex at (1, 0) and passes through the points (negative 4, 1) and (6, 1). Another branch opens downward with vertex at (1, negative 2) and passes through the points (negative 4.5, negative 3) and (6, negative 3). All values are estimated.

An equation reads, 9 left parenthesis y plus 1 right parenthesis squared minus left parenthesis x minus 1 right parenthesis squared equals 9.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find a hyperbola's foci and vertices.

22) Find the general equation of the hyperbola from the given graph.

A horizontal hyperbola and two asymptotes are graphed on an x y coordinate plane. The x axis ranges from negative 10 to 5, in increments of 1. The y axis ranges from negative 4 to 8, in increments of 1. The hyperbola has two branches. One branch opens leftward with vertex at (negative 6, 2) and passes through the points (negative 8, 5) and (negative 9, negative 1). Another branch opens rightward with vertex at (0, 2) and passes through the points (4, 6) and (4, negative 2). The first asymptote is an upward sloping dashed line that passes through (negative 6, 0), (negative 3, 2), and (4, 0). The second asymptote is a downward sloping dashed line that passes through (negative 6, 4), (negative 3, 2), and (3, negative 2). All values are estimated.

An equation reads, 4 x squared plus 9 y squared plus 24 x minus 36 y plus 36 equals 0.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Graph a hyperbola using asymptotes as graphing aids.

23) Find the standard form of the equation of the hyperbola from the given graph.

A horizontal hyperbola and two asymptotes are graphed on an x y coordinate plane. The x axis ranges from negative 8 to 10, in increments of 2. The y axis ranges from negative 3 to 4, in increments of 1. The hyperbola has two branches. One branch opens leftward with vertex at (negative 2, 1) and passes through the points (negative 6, 3) and (negative 6, negative 1). Another branch opens rightward with vertex at (4, 1) and passes through the points (8, 3) and (8, negative 1). The first asymptote is an upward sloping dashed line that passes through (negative 2, 0), (1, 1), and (4, 2). The second asymptote is a downward sloping dashed line that passes through (negative 2, 2), (1, 1), and (4, 0). All values are estimated.

A)

An equation reads, start fraction left parenthesis x minus 1 right parenthesis squared over 9 end fraction minus left parenthesis y minus 1 right parenthesis squared equals 1.

B)

An equation reads, start fraction left parenthesis y minus 1 right parenthesis squared over 9 end fraction minus left parenthesis x plus 1 right parenthesis squared equals 1.

C)

An equation reads, left parenthesis y plus 1 right parenthesis squared minus start fraction left parenthesis x minus 1 right parenthesis squared over 9 end fraction equals 1.

D)

An equation reads, left parenthesis x minus 1 right parenthesis squared minus start fraction left parenthesis y minus 1 right parenthesis squared over 9 end fraction equals 1.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Graph a hyperbola using asymptotes as graphing aids.

24) Find the equation of the hyperbola from the given graph.

A horizontal hyperbola and two asymptotes are graphed on an x y coordinate plane. The x axis ranges from negative 8 to 10, in increments of 2. The y axis ranges from negative 3 to 4, in increments of 1. The hyperbola has two branches. One branch opens leftward with vertex at (negative 2, 1) and passes through the points (negative 5, 3) and (negative 5, negative 0.5). Another branch opens rightward with vertex at (4, 1) and passes through the points (6, 2.5) and (7, negative 0.5). The first asymptote is an upward sloping dashed line that passes through (negative 2, 0), (1, 1), and (4, 2). The second asymptote is a downward sloping dashed line that passes through (negative 2, 2), (1, 1), and (4, 0). All values are estimated.

A)

An equation reads, left parenthesis x minus 1 right parenthesis squared minus 9 left parenthesis y minus 1 right parenthesis squared equals 9.

B)

An equation reads, left parenthesis y minus 1 right parenthesis squared minus 9 left parenthesis x plus 1 right parenthesis squared equals 9.

C)

An equation reads, 9 left parenthesis y plus 1 right parenthesis squared minus left parenthesis x minus 1 right parenthesis squared equals 9.

D)

An equation reads, 9 left parenthesis x minus 1 right parenthesis squared minus left parenthesis y minus 1 right parenthesis squared equals 9.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Graph a hyperbola using asymptotes as graphing aids.

25) Find the general equation of the hyperbola from the given graph.

A horizontal hyperbola and two asymptotes are graphed on an x y coordinate plane. The x axis ranges from negative 8 to 12 in increments of 2. The y axis ranges from negative 2 to 6 in increments of 0.5. The hyperbola has two branches. One branch opens leftward with vertex at (negative 2, 3) and passes through the points (negative 7, 5) and (negative 7, 1). Another branch opens rightward with vertex at (6, 3) and passes through the points (11, 5) and (11, 1). The first asymptote is an upward sloping dashed line. The second asymptote is a downward sloping dashed line. Both the asymptotes intersect at (2, 3). All values are estimated.

A)

An equation reads, x squared plus 16 y squared minus 4 x minus 96 y plus 132 equals 0.

B)

An equation reads, 16 x squared plus y squared minus 64 x minus 6 y plus 57 equals 0.

C)

An equation reads, x squared plus 16 y squared plus 6 x minus 64 y plus 57 equals 0.

D)

An equation reads, 16 x squared plus y squared plus 96 x minus 4 y plus 132 equals 0.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Graph a hyperbola using asymptotes as graphing aids.

26) Graph the hyperbola.

An equation reads, start fraction left parenthesis x minus 2 right parenthesis squared over 16 end fraction minus left parenthesis y minus 3 right parenthesis squared equals 1.

A)

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 12 in increments of 2. The y axis ranges from negative 2 to 6 in increments of 0.5. The hyperbola has two branches. One branch opens leftward with vertex at (negative 2, 3) and passes through the points (negative 4, 4) and (negative 4, 2). Another branch opens rightward with vertex at (6, 3) and passes through the points (10, 4.5) and (8, 2). All values are estimated.

B)

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 2 to 6 in increments of 0.5. The y axis ranges from negative 8 to 12 in increments of 2. The hyperbola has two branches. One branch opens leftward with vertex at (1, 3) and passes through the points (0,10) and (negative 4, 0). Another branch opens rightward with vertex at (3, 3) and passes through the points (4, 10) and (4, negative 4). All values are estimated.

C)

A vertical hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 14 to 8 in increments of 2. The y axis ranges from negative 2 to 6 in increments of 0.5. The hyperbola has two branches. One branch opens upward with vertex at (negative 3, 3) and passes through the points (negative 12, 4.5) and (4, 4). Another branch opens downward with vertex at (negative 3, 1) and passes through the points (negative 10, 0) and (4, 0). All values are estimated.

D)

A vertical hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 2 in increments of 0.5. The y axis ranges from negative 14 to 14 in increments of 2. The hyperbola has two branches. One branch opens upward with vertex at (negative 3, 6) and passes through the points (negative 5, 10) and (negative 1, 10.5). Another branch opens downward with vertex at (negative 3, negative 1) and passes through the points (negative 6, negative 10) and (0, negative 10.5). All values are estimated.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find a hyperbola's foci and vertices.

27) Graph the hyperbola.

An equation reads, 4 left parenthesis y plus 1 right parenthesis squared minus left parenthesis x plus 2 right parenthesis squared equals 4.

A)

A vertical hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 4 in increments of 1. The y axis ranges from negative 4 to 3 in increments of 0.5. The hyperbola has two branches. One branch opens upward with vertex at (negative 2, 0) and passes through the points (negative 5, 1) and (2, 1). Another branch opens downward with vertex at (negative 2, negative 2) and passes through the points (negative 6, negative 3) and (2.5, negative 3.5). All values are estimated.

B)

A vertical hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 2 in increments of 0.5. The y axis ranges from negative 8 to 8 in increments of 1. The hyperbola has two branches. One branch opens upward with vertex at (negative 2, 1) and passes through the points (negative 5, 5.5) and (0, 3.5). Another branch opens downward with vertex at (negative 2, negative 3) and passes through the points (negative 4, negative 5) and (0, negative 5.5). All values are estimated.

C)

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 8 in increments of 1. The y axis ranges from negative 4 to 6 in increments of 0.5. The hyperbola has two branches. One branch opens leftward with vertex at (negative 1, 2) and passes through the points (negative 5, 5) and (negative 5, negative 1). Another branch opens rightward with vertex at (3, 2) and passes through the points (6, 4) and (7, negative 1). All values are estimated.

D)

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 6 in increments of 0.5. The y axis ranges from negative 4 to 6 in increments of 0.5. The hyperbola has two branches. One branch opens leftward with vertex at (0, 2) and passes through the points (negative 0.5, 4) and (negative 0.5, 0). Another branch opens rightward with vertex at (2, 2) and passes through the points (2.5, 3.5) and (2.5, 0). All values are estimated.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find a hyperbola's foci and vertices.

28) Graph the hyperbola.

An equation reads, x squared plus 4 y squared plus 4 x plus 8 y plus 4 equals 0.

A)

A vertical hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 4 in increments of 1. The y axis ranges from negative 4 to 3 in increments of 0.5. The hyperbola has two branches. One branch opens upward with vertex at (negative 2, 0) and passes through the points (negative 5, 1) and (2, 1). Another branch opens downward with vertex at (negative 2, negative 2) and passes through the points (negative 4, negative 2.5) and (2.5, negative 3.5). All values are estimated.

B)

A vertical hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 2 in increments of 0.5. The y axis ranges from negative 8 to 8 in increments of 1. The hyperbola has two branches. One branch opens upward with vertex at (negative 2, 1) and passes through the points (negative 5, 5.5) and (0, 3.5). Another branch opens downward with vertex at (negative 2, negative 3) and passes through the points (negative 4, negative 5) and (0, negative 5.5). All values are estimated.

C)

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 8 in increments of 1. The y axis ranges from negative 4 to 6 in increments of 0.5. The hyperbola has two branches. One branch opens leftward with vertex at (negative 1, 2) and passes through the points (negative 5, 5) and (negative 5, negative 1). Another branch opens rightward with vertex at (3, 2) and passes through the points (6, 4) and (7, negative 1). All values are estimated.

D)

A horizontal hyperbola is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 6 in increments of 0.5. The y axis ranges from negative 4 to 6 in increments of 0.5. The hyperbola has two branches. One branch opens leftward with vertex at (0, 2) and passes through the points (negative 0.5, 4) and (negative 0.5, 0). Another branch opens rightward with vertex at (2, 2) and passes through the points (2.5, 3.5) and (2.5, 0). All values are estimated.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find a hyperbola's foci and vertices.

29) Two loran stations are located 270 miles apart along a coast. If a ship records a time difference of 0.00047 second and continues on the hyperbolic path corresponding to that difference, where will it reach shore? Round to the nearest mile. (Assume the speed of the radio signal is 186,000 miles per second.)

A) The ship reaches shore between the two stations, 183 miles from one station and 357 miles from the other.

B) The ship reaches shore between the two stations, 91 miles from one station and 179 miles from the other.

C) The ship reaches shore between the two stations, 226 miles from one station and 314 miles from the other.

D) The ship reaches shore between the two stations, 248 miles from one station and 292 miles from the other.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Solve applied problems that involve hyperbolas.

30) Find the standard form of the equation of a hyperbola with foci (6, 13) and (6, -11), and vertices (6, 6) and (6, -4).

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the point (h, k).

31) Find the standard form of the equation of a hyperbola with foci (8, 0) and (-8, 0), and vertices (3, 0) and (-3, 0).

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 04

Learning Objective: Find the equation of a hyperbola centered at the point (h, k).

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Document Type:
DOCX
Chapter Number:
8
Created Date:
Aug 21, 2025
Chapter Name:
Chapter 8 Conics And Systems Of Nonlinear Equations And Inequalities
Author:
Cynthia Y. Young

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