Deck 62: Hyperbolas

Question 1

Find the center,vertices and foci of the hyperbola.​ $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$ ​

A)Center: (0,0) Vertices: $( \pm 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$
B)Center: (0,0) Vertices: $( 0 , \pm 4 )$
Foci: $( 0 , \pm \sqrt { 41 } )$
C)Center: $( 16,25 )$ Vertices: $( \pm 5,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$
D)Center: (0,0) Vertices: $( \pm 5,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$
E)Center: $( 16,25 )$ Vertices: $( \pm 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$

Answer 1

Center: (0,0) Vertices: $( \pm 5,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$

Question 2

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola.​ $$\frac { ( x + 5 ) ^ { 2 } } { 121 } - \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$$ ​

A)Center: $$( - 5,4 )$$ ​
B)Center: (5,4) ​
C)Center: (0,0)
D)Center: $$( - 5 , - 4 )$$ ​
E)Center: (0,0) ​

Answer 2

Center: $$( - 5,4 )$$ ​

Question 3

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Foci: $$( \pm 10,0 )$$ ;asymptotes: $y = \pm \frac { 3 } { 4 } x$ ​

A) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 64 } = 1$
B) $$\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 36 } = 1$$
C) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$
D) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 36 } = 1$
E) $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 64 } = 1$

Answer 3

$$\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 36 } = 1$$

Question 4

Find the center,vertices and foci of the hyperbola.​ $26 y ^ { 2 } - 23 x ^ { 2 } = 598$ ​

A)Center: (0,0) Vertices: $( 0 , \pm \sqrt { 7 } )$
Foci: $( 0 , \pm \sqrt { 49 } )$
B)Center: $( 23,26 )$ ​ Vertices: $( 0 , \pm \sqrt { 7 } )$
Foci: $( 0 , \pm \sqrt { 49 } )$
C)Center: (0,0) Vertices: $( \pm \sqrt { 49 } , 0 )$
Foci: $( 0 , \pm \sqrt { 49 } )$
D)Center: (0,0) Vertices: $( \pm \sqrt { 7 } , 0 )$
Foci: $( \pm \sqrt { 49 } , 0 )$
E)Center: $( 26,23 )$ Vertices: $( 0 , \pm \sqrt { 7 } )$
Foci: $( 0 , \pm \sqrt { 49 } )$

Question 5

Find the center,vertices and foci of the hyperbola.​ $$\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 1 } = 1$$ ​

A)Center: (0,0) Vertices: $( 0 , \pm 2 )$
Foci: $( 0 , \pm \sqrt { 5 } )$
B)Center: (0,0) Vertices: $( \pm 2,0 )$
Foci: $( 0 , \pm \sqrt { 5 } )$
C)Center: $( 4,1 )$ Vertices: $( \pm 2,0 )$
Foci: $( \pm \sqrt { 5 } , 0 )$
D)Center: $( 4,1 )$ Vertices: $( 0 , \pm 2 )$
Foci: $( 0 , \pm \sqrt { 5 } )$
E)Center: (0,0) Vertices: $( \pm 2,0 )$
Foci: $( \pm \sqrt { 5 } , 0 )$

Question 6

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola.​ $$\frac { ( y - 5 ) ^ { 2 } } { 1 / 64 } - \frac { ( x + 3 ) ^ { 2 } } { 1 / 49 } = 1$$ ​

A)Center: (-3,5) ​
B)Center: (0,0) ​
C)Center: (3,- 5)
D)Center: (0,0)
E)Center: (3,5)

Question 7

Find the center,vertices and foci of the hyperbola.​ $21 x ^ { 2 } - 5 y ^ { 2 } = 105$ ​

A)Center: (0,0) Vertices: (0,0)
Foci: $( \sqrt { 21 } , 0 )$
B)Center: (0,0) Vertices: $( 0 , \pm \sqrt { 5 } )$
Foci: $( \pm \sqrt { 26 } , 0 )$
C)Center: (0,0) Vertices: $( \pm \sqrt { 5 } , 0 )$
Foci: $( \pm \sqrt { 26 } , 0 )$
D)Center: (0,0) Vertices: $( - \sqrt { 5 } , 0 )$
Foci: $( \pm \sqrt { 26 } , 0 )$
E)Center: (0,0) Vertices: $$( 0 , \pm \sqrt { 5 } )$$
Foci: $( 0 , \pm \sqrt { 26 } )$

Question 8

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola.​ $$\frac { ( y + 3 ) ^ { 2 } } { 1 / 81 } - \frac { ( x - 2 ) ^ { 2 } } { 1 / 64 } = 1$$ ​

A)Center: (2,- 3)
B)Center: (0,0)
C)Center: (2,- 3)
D)Center: (0,0) ​
E)Center: (2,- 3)

Question 9

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: $( 0 , \pm 14 )$ ;asymptotes: $y = \pm 7 x$ ​

A) $$\frac { x ^ { 2 } } { 196 } + \frac { y ^ { 2 } } { 4 } = 1$$
B) $\frac { y ^ { 2 } } { 196 } - \frac { x ^ { 2 } } { 4 } = 1$
C) $\frac { y ^ { 2 } } { 4 } + \frac { x ^ { 2 } } { 196 } = 1$
D) $\frac { 196 x ^ { 2 } } { 4 } - \frac { 4 y ^ { 2 } } { 196 } = 1$
E) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 196 } = 1$

Question 10

Find the center,vertices and foci of the hyperbola.​ $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 1$ ​

A)Center: (0,0) Vertices: $( 0,6 )$
Foci: $( 0 , \sqrt { 61 } )$
B)Center: (0,0) Vertices: $( \pm 6,0 )$
Foci: $( \pm \sqrt { 61 } , 0 )$
C)Center: (0,0) Vertices: $( \pm 6,0 )$
Foci: $( \sqrt { 61 } , 0 )$
D)Center: (0,0) Vertices: $( 6,0 )$
Foci: $( \pm \sqrt { 61 } , 0 )$
E)Center: (0,0) Vertices: $( 0 , \pm 5 )$
Foci: $( 0 , \pm \sqrt { 61 } )$

Question 11

Find the center,vertices and foci of the hyperbola.​ $3 x ^ { 2 } - 4 y ^ { 2 } = 12$ ​

A)Center: (1,1) Vertices: (±4,0)
Foci: $( \pm \sqrt { 7 } , 0 )$ ​
B)Center: $( 3,4 )$ Vertices: (±4,0)
Foci: $( \pm \sqrt { 7 } , 0 )$
C)Center: (0,0) Vertices: (0,± $2$ )
Foci: $( 0 , \pm \sqrt { 7 } )$
D)Center: (1,1) Vertices: (0,± $2$ )
Foci: $( 0 , \pm \sqrt { 7 } )$
E)Center: (0,0) Vertices: (± $2$ ,0)
Foci: $( \pm \sqrt { 7 } , 0 )$

Question 12

Find the center,vertices and foci of the hyperbola.​ $5 x ^ { 2 } - 6 y ^ { 2 } = 30$ ​

A)Center: (1,1) Vertices: $( 0 , \pm \sqrt { 6 } )$
Foci: $( 0 , \pm \sqrt { 11 } )$
B)Center: $( 5,6 )$ Vertices: $( \pm \sqrt { 6 } , 0 )$
Foci: $( \pm \sqrt { 11 } , 0 )$
C)Center: (0,0) Vertices: $( 0 , \pm \sqrt { 6 } )$
Foci: $( 0 , \pm \sqrt { 11 } )$
D)Center: (0,0) Vertices: $( \pm \sqrt { 6 } , 0 )$
Foci: $( \pm \sqrt { 11 } , 0 )$
E)Center: $$( 6,5 )$$ Vertices: $( \pm \sqrt { 6 } , 0 )$
Foci: $( \pm \sqrt { 11 } , 0 )$

Question 13

Select the correct graph of the following equations of the hyperbola and find the center of hyperbola.​ $$\frac { ( x - 6 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { 1 } = 1$$ ​

A)Center: (0,0) ​
B)Center: (0,0) ​
C)Center: $$( 6,2 )$$ ​
D)Center: (0,0) ​
E)Center: $$( 6 , - 2 )$$ ​

Question 14

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: $( \pm 2,0 )$ ;asymptotes: $y = \pm 7 x$ ​

A) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 196 } = 1$
B) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 196 } = 1$
C) $\frac { y ^ { 2 } } { 4 } + \frac { x ^ { 2 } } { 196 } = 1$
D) $\frac { y ^ { 2 } } { 196 } - \frac { x ^ { 2 } } { 4 } = 1$
E) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 196 } = 1$

Question 15

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: $( 0 , \pm 6 )$ ;asymptotes: $y = \pm 6 x$ ​

A) $\frac { y ^ { 2 } } { 1 } - \frac { x ^ { 2 } } { 36 } = 1$
B) $$\frac { y ^ { 2 } } { 36 } + \frac { x ^ { 2 } } { 1 } = 1$$
C) $$\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 1 } = 1$$
D) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 1 } = 1$
E) $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 1 } = 1$

Question 16

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: $( 0 , \pm 5 )$ ;foci: $( 0 , \pm 9 )$ ​

A) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 56 } = 1$
B) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 56 } = 1$
C) $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 56 } = 1$
D) $\frac { y ^ { 2 } } { 56 } - \frac { x ^ { 2 } } { 25 } = 1$
E) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 56 } = 1$

Question 17

Find the standard form of the equation of the hyperbola with the given characteristics. ​
Vertices: (6,0), (10,0);foci: (0,0), (12,0)
​

A) $\frac { ( x - 8 ) ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 20 } = 1$
B) $\frac { y ^ { 2 } } { 20 } - \frac { ( x - 8 ) ^ { 2 } } { 4 } = 1$
C) $\frac { ( x - 8 ) ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 20 } = 1$
D) $\frac { y ^ { 2 } } { 4 } - \frac { ( x - 8 ) ^ { 2 } } { 20 } = 1$
E) $\frac { y ^ { 2 } } { 20 } + \frac { ( x - 8 ) ^ { 2 } } { 4 } = 1$

Question 18

Find the center,vertices and foci of the hyperbola.​ $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$ ​

A)Center: (0,0) Vertices: $( 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$
B)Center: (0,0) Vertices: $$( - 4,0 )$$
Foci: $( - \sqrt { 41 } , 0 )$
C)Center: (0,0) Vertices: $( 4,0 )$
Foci: $( - \sqrt { 41 } , 0 )$
D)Center: (0,0) Vertices: $( 4,0 )$
Foci: $$( \sqrt { 41 } , 0 )$$
E)Center: (0,0) Vertices: $( \pm 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$

Question 19

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: $( \pm 4,0 )$ ;foci: $( \pm 8,0 )$ ​

A) $\frac { y ^ { 2 } } { 48 } - \frac { x ^ { 2 } } { 16 } = 1$
B) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 48 } = 1$
C) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 48 } = 1$
D) $\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 48 } = 1$
E) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$

Question 20

Find the center,vertices and foci of the hyperbola.​ $\frac { y ^ { 2 } } { 1 } - \frac { x ^ { 2 } } { 36 } = 1$ ​

A)Center: (0,0) Vertices: $( 0 , \pm 1 )$
Foci: $( 0 , \pm \sqrt { 37 } )$
B)Center: $( 36,1 )$ Vertices: $( 0 , \pm \sqrt { 37 } )$
Foci: $( 0 , \pm 1 )$
C)Center: (0,0) Vertices: $( \pm 1,0 )$
Foci: $( \pm \sqrt { 37 } , 0 )$
D)Center: $( 36,1 )$ Vertices: ​ $( 0 , \pm 1 )$
Foci: $( 0 , \pm \sqrt { 37 } )$
E)Center: $( 36,1 )$ Vertices: $( \pm 1,0 )$
Foci: $( \pm \sqrt { 37 } , 0 )$

Question 21

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$x ^ { 2 } + y ^ { 2 } - 7 x + 2 y - 12 = 0$$ ​

A)Parabola
B)Hyperbola
C)Ellipse
D)Circle
E)None of the above

Question 22

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$3 y ^ { 2 } + 3 x ^ { 2 } - 21 x + 34 = 0$$ ​

A)Hyperbola
B)Circle
C)Ellipse
D)Parabola
E)None of the above

Question 23

Select the correct equation of the following graph.​ ​

A) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$
B) $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 36 } = 1$
C) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 36 } = 1$
D) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 0$
E) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$

Question 24

Select the correct equation of the following graph.​ ​

A) $\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 49 } = 1$
B) $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 49 } = 1$
D) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 49 } = 1$
E) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$

Question 25

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$8 x ^ { 2 } - 4 y ^ { 2 } - 16 x - 3 = 0$$ ​

A)Circle
B)Ellipse
C)Hyperbola
D)Parabola
E)None of the above

Question 26

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$x ^ { 2 } + y ^ { 2 } - 9 x + 3 y - 16 = 0$$ ​

A)Circle
B)Parabola
C)Ellipse
D)Hyperbola
E)None of the above

Question 27

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$y ^ { 2 } + 8 x + 5 y + 26 = 0$$ ​

A)Ellipse
B)Hyperbola
C)Circle
D)Parabola
E)None of the above

Question 28

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$x ^ { 2 } - 6 x - 3 y + 8 = 0$$ ​

A)Circle
B)Parabola
C)Hyperbola
D)Ellipse
E)None of the above

Question 29

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$4 x ^ { 2 } + 3 y ^ { 2 } + 5 x - 28 y + 58 = 0$$ ​

A)Hyperbola
B)Circle
C)Ellipse
D)Parabola
E)None of the above

Question 30

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$9 x ^ { 2 } + 36 y ^ { 2 } - 20 x + 256 y - 535 = 0$$ ​

A)Hyperbola
B)Ellipse
C)Circle
D)Parabola
E)None of the above

Question 31

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$22 x ^ { 2 } - 13 x - 200 y - 112 = 0$$ ​

A)Hyperbola
B)Circle
C)Parabola
D)Ellipse
E)None of the above

Question 32

Identify the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$16 x ^ { 2 } + 9 y ^ { 2 } - 98 x + 5 y + 224 = 0$$ ​

A)Ellipse
B)Parabola
C)Hyperbola
D)Circle
E)None of the above

Question 33

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$25 x ^ { 2 } + 64 y ^ { 2 } - 14 x + 17 y - 119 = 0$$ ​

A)Parabola
B)Circle
C)Hyperbola
D)Ellipse
E)None of the above

Question 34

You and a friend live 4 miles apart (on the same "east-west" street)and are talking on the phone.You hear a clap of thunder from lightning in a storm,and 16 seconds later your friend hears the thunder.Find an equation that gives the possible places where the lightning could have occurred.(Assume that the coordinate system is measured in feet and that sound travels at 1100 feet per second. )
​

A) $\frac { x ^ { 2 } } { 34,073,600 } + \frac { y ^ { 2 } } { 77,440,000 } = 1$
B) $\frac { x ^ { 2 } } { 34,073,600 } - \frac { y ^ { 2 } } { 77,440,000 } = 1$
C) $\frac { y ^ { 2 } } { 77,440,000 } - \frac { x ^ { 2 } } { 34,073,600 } = 1$
D) $\frac { x ^ { 2 } } { 77,440,000 } - \frac { y ^ { 2 } } { 34,073,600 } = 1$
E) $\frac { x ^ { 2 } } { 77,440,000 } + \frac { y ^ { 2 } } { 34,073,600 } = 1$

Question 35

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$y ^ { 2 } - 9 y - 4 x - 21 = 0$$ ​

A)Parabola
B)Circle
C)Hyperbola
D)Ellipse
E)None of the above

Question 36

Identify the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$3 x ^ { 2 } - 3 y ^ { 2 } - 3 x + 6 y + 17 = 0$$ ​

A)Circle
B)Hyperbola
C)Ellipse
D)Parabola
E)None of the above

Question 37

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$100 x ^ { 2 } + 100 y ^ { 2 } - 100 x + 400 y + 403 = 0$$ ​

A)Parabola
B)Hyperbola
C)Circle
D)Ellipse
E)None of the above

Question 38

Select the correct equation of the following graph.​ ​

A) $\frac { ( x - 1 ) ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$
B) $\frac { ( x - 1 ) ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 25 } = 1$
C) $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$
D) $\frac { ( x - 1 ) ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = 1$
E) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = 1$

Question 39

Identify the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$27 x ^ { 2 } - 18 x - 200 y - 119 = 0$$ ​

A)Parabola
B)Hyperbola
C)Circle
D)Ellipse
E)None of the above

Question 40

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$y ^ { 2 } - 4 x ^ { 2 } + 4 x - 8 y - 24 = 0$$ ​

A)Hyperbola
B)Parabola
C)Circle
D)Ellipse
E)None of the above

Question 41

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$2 x ^ { 2 } - y ^ { 2 } + 2 x + 5 y - 6 = 0$$ ​

A)Ellipse
B)Hyperbola
C)Parabola
D)Circle
E)None of the above

Question 42

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (-10,-2), (0,-2)
Asymptotes: y = ± $\frac { 4 } { 5 }$ x
​

A) $\frac { ( x + 5 ) ^ { 2 } } { 25 } - \frac { ( y + 2 ) ^ { 2 } } { 16 } = 0$
B) $\frac { ( x + 5 ) ^ { 2 } } { 25 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$
C) $\frac { ( y + 5 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 16 } = 1$
D) $\frac { ( y - 2 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 16 } = 1$
E) $\frac { ( x + 5 ) ^ { 2 } } { 25 } - \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$

Question 43

Find the vertices and asymptotes of the hyperbola. $9 y ^ { 2 } - 16 x ^ { 2 } = 144$

A)vertices: (0,±4​)asymptote: $y = \pm \frac { 3 } { 4 } x$
B)vertices: (±4,3)asymptote: $y = \pm \frac { 4 } { 3 } x$
C)vertices: (±4,0)asymptote: $y = \pm \frac { 4 } { 3 } x$
D)vertices: (±3,0)asymptote: $$y = \pm \frac { 3 } { 4 } x$$
E)vertices: (0,±3)asymptote: $$y = \pm \frac { 4 } { 3 } x$$

Question 44

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (3,3), (3,7)
Foci: (3,1), (3,9)
​

A) $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x - 3 ) ^ { 2 } } { 12 } = 1$
B) $\frac { ( y - 5 ) ^ { 2 } } { 4 } + \frac { ( x - 3 ) ^ { 2 } } { 12 } = 1$
C) $\frac { ( x - 5 ) ^ { 2 } } { 4 } - \frac { ( y - 3 ) ^ { 2 } } { 12 } = 1$
D) $\frac { ( y + 5 ) ^ { 2 } } { 4 } - \frac { ( x - 3 ) ^ { 2 } } { 12 } = 1$
E) $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x + 3 ) ^ { 2 } } { 12 } = 1$

Question 45

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: $( 0 , \pm 6 )$ foci: $( 0 , \pm 8 )$

A) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 64 } = 1$
B) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 28 } = 1$
C) $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 28 } = 1$
D) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 28 } = 1$
E) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 28 } = 64$

Question 46

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 4,0 )$ asymptotes: $y = \pm 2 x$

A) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 4 } = 1$
B) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 4 } = 1$
C) $\frac { y ^ { 2 } } { \frac { 16 } { 5 } } - \frac { x ^ { 2 } } { \frac { 64 } { 5 } } = 1$
D) $\frac { x ^ { 2 } } { \frac { 16 } { 5 } } - \frac { y ^ { 2 } } { \frac { 64 } { 5 } } = 1$
E) $\frac { x ^ { 2 } } { \frac { 64 } { 5 } } - \frac { y ^ { 2 } } { \frac { 16 } { 5 } } = 1$

Question 47

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: $( 0 , \pm 3 )$ foci: $( 0 , \pm 6 )$

A) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 27 } = 1$
B) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$
C) $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 27 } = 1$
D) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 27 } = 36$
E) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 27 } = 36$

Question 48

Find the vertices and asymptotes of the hyperbola.​ $$\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 100 } = 1$$

A)vertices: $( \pm 7,0 )$ asymptote: $$y = \pm \frac { 7 } { 10 } x$$
B)vertices: $$( 0 , \pm 7 )$$ asymptote: $y = \pm \frac { 10 } { 7 } x$
C)vertices: $( \pm 7,0 )$ asymptote: $y = \pm \frac { 10 } { 7 } x$
D)vertices: $( \pm 7,10 )$ asymptote: $y = \pm \frac { 10 } { 7 } x$
E)vertices: $( 10 , \pm 7 )$ asymptote: $y = \pm \frac { 10 } { 7 } x$

Question 49

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 4,0 )$ asymptotes: $y = \pm 5 x$

A) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$
B) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 16 } = 1$
C) $\frac { y ^ { 2 } } { \frac { 16 } { 26 } } - \frac { x ^ { 2 } } { \frac { 400 } { 26 } } = 1$
D) $\frac { x ^ { 2 } } { \frac { 16 } { 26 } } - \frac { y ^ { 2 } } { \frac { 400 } { 26 } } = 1$
E) $\frac { x ^ { 2 } } { \frac { 400 } { 26 } } - \frac { y ^ { 2 } } { \frac { 16 } { 26 } } = 1$

Question 50

Graph the hyperbola.​ $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 25 } = 1$ ​

A)​
B)​
C)​
D)​

Question 51

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (1,-2), (5,-2)
Asymptotes: $y = \frac { 5 } { 2 } x , y = - \frac { 5 } { 2 } x$

A) $\frac { ( y - 3 ) ^ { 2 } } { 4 } - \frac { ( x + 2 ) ^ { 2 } } { 25 } = 1$
B) $\frac { ( x - 3 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$
C) $\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$
D) $\frac { ( x - 3 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$
E) $\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1$

Question 52

Graph the hyperbola.​ $$9 y ^ { 2 } - 16 x ^ { 2 } + 36 y + 64 x = 172$$ ​

A)​
B)​
C)​
D)​

Question 53

Find the vertices and asymptotes of the hyperbola.​ $16 y ^ { 2 } - 9 x ^ { 2 } = 144$ ​

A)​vertices: (0,±3)asymptote: $y = \pm \frac { 3 } { 4 } x$
B)​​vertices: (0,±3)asymptote: $y = \pm \frac { 4 } { 3 } x$
C)​vertices: (±3,0)asymptote: $y = \pm \frac { 3 } { 4 } x$
D)​​vertices: (±3,0)asymptote: $y = \pm \frac { 4 } { 3 } x$
E)​vertices: (±3,4)asymptote: $y = \pm \frac { 3 } { 4 } x$

Question 54

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (5,-6), (5,-2)
Foci: (5,-7), (5,-1)
​

A) $\frac { ( y + 4 ) ^ { 2 } } { 4 } - \frac { ( x - 5 ) ^ { 2 } } { 5 } = 1$
B) $\frac { ( y + 4 ) ^ { 2 } } { 4 } + \frac { ( x - 5 ) ^ { 2 } } { 5 } = 1$
C) $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x + 4 ) ^ { 2 } } { 5 } = 1$
D) $\frac { ( y + 5 ) ^ { 2 } } { 4 } - \frac { ( x - 4 ) ^ { 2 } } { 5 } = 1$
E) $\frac { ( y - 4 ) ^ { 2 } } { 4 } - \frac { ( x + 5 ) ^ { 2 } } { 9 } = 1$

Question 55

Find the center and vertices of the hyperbola. $12 x ^ { 2 } - 4 y ^ { 2 } - 72 x - 16 y + 44 = 0$

A)center: (3,-2),vertices: (3,-4), (3,0)
B)center: (-3,2),vertices: (-3,0), (-3,4)
C)center: (3,-2),vertices: (1,-2), (5,-2)
D)center: (2,-3),vertices: (0,-3), (4,-3)
E)center: (-3,2),vertices: (-5,2), (-1,2)

Question 56

Find the center and foci of the hyperbola. $\frac { ( y - 8 ) ^ { 2 } } { 9 } - \frac { ( x + 5 ) ^ { 2 } } { 27 } = 1$

A)center: (-5,8),foci: (-11,8), (1,8)
B)center: (-5,8),foci: (-5,2), (-5,14)
C)center: (-8,5),foci: (-8,-1), (-8,11)
D)center: (8,-5),foci: (2,-5), (14,-5)
E)center: (5,-8),foci: (5,-14), (5,-2)

Question 57

Select the correct equation of the following graph. ​​ ​

A) $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$
B) $\frac { ( x - 1 ) ^ { 2 } } { 4 } - \frac { ( y - 2 ) ^ { 2 } } { 25 } = 0$
C) $\frac { x ^ { 2 } } { 25 } - \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$
D) $\frac { ( x - 1 ) ^ { 2 } } { 4 } - \frac { ( y - 2 ) ^ { 2 } } { 25 } = 1$
E) $\frac { ( x - 1 ) ^ { 2 } } { 25 } - \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$

Question 58

Graph the hyperbola.​ $$4 x ^ { 2 } - 16 y ^ { 2 } = 64$$ ​

A)​
B)​
C)​
D)​

Question 59

Find the vertices and asymptotes of the hyperbola. $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 81 } = 1$

A)vertices: (0,±8)asymptote: y = ± $\frac { 9 } { 8 }$ x
B)vertices: (0,±8)asymptote: y = ± $\frac { 8 } { 9 }$ x
C)vertices: (±8,0)asymptote: y = ± $\frac { 9 } { 8 }$ x
D)vertices: (±8,0)asymptote: y = ± $\frac { 8 } { 9 }$ x
E)vertices: (±8,9)asymptote: y = ± $\frac { 8 } { 9 }$ x

Question 60

Find the center and vertices of the hyperbola. $12 x ^ { 2 } - 4 y ^ { 2 } - 48 x + 32 y - 64 = 0$

A)center: (-2,-4),vertices: (-2,-6), (-2,-2)
B)center: (2,4),vertices: (2,2), (2,6)
C)center: (2,4),vertices: (0,4), (4,4)
D)center: (-2,-4),vertices: (-4,-4), (0,-4)
E)center: (-4,-2),vertices: (-6,-2), (-2,-2)

Question 61

Write the equation of the hyperbola with vertices (4,0), (-4,0)and focus (5,0).

Question 62

Find the equation of the hyperbola with vertices (2,0), (-2,0)and focus (4,0). ​

A) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 12 } = 1$
B) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 12 } = 1$
C) $\frac { x ^ { 2 } } { 12 } - \frac { y ^ { 2 } } { 4 } = 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 12 } = 1$
E)none of these