Question 1

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

Accepted Answer

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 
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 C

Question 2

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

Accepted Answer

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)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 56 } = 1$ 
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)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 56 } = 1$ A

Question 3

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

Accepted Answer

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: $y = \pm \frac { 10 } { 7 } x$ 
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: $y = \pm \frac { 10 } { 7 } x$ C

Question 4

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

Accepted Answer

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)  $\frac { x ^ { 2 } } { \frac { 400 } { 26 } } - \frac { y ^ { 2 } } { \frac { 16 } { 26 } } = 1$ 
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 5

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

Accepted Answer

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: $y = \pm \frac { 3 } { 4 } x$ 
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 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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)  $\frac { x ^ { 2 } } { \frac { 64 } { 5 } } - \frac { y ^ { 2 } } { \frac { 16 } { 5 } } = 1$ 
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 8

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

Accepted Answer

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)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 196 } = 1$ 
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 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 196 } = 1$ 
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 12

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

Accepted Answer

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)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 27 } = 36$ 
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 13

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

Accepted Answer

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)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$ 
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 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

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)
​

Accepted Answer

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)  $\frac { y ^ { 2 } } { 20 } + \frac { ( x - 8 ) ^ { 2 } } { 4 } = 1$ 
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 and vertices of the hyperbola. $12 x ^ { 2 } - 4 y ^ { 2 } - 48 x + 32 y - 64 = 0$

Accepted Answer

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) 
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 19

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

Accepted Answer

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

Question 20

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
​

Accepted Answer

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)  $\frac { ( x + 5 ) ^ { 2 } } { 25 } - \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ 
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)  $\frac { ( x + 5 ) ^ { 2 } } { 25 } - \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$

Exam 62: Hyperbolas

Find the vertices and asymptotes of the hyperbola. x264−y281=1\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 81 } = 164x2​−81y2​=1

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

Find the vertices and asymptotes of the hyperbola.​ x249−y2100=1\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 100 } = 149x2​−100y2​=1

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

Find the vertices and asymptotes of the hyperbola.​ 16y2−9x2=14416 y ^ { 2 } - 9 x ^ { 2 } = 14416y2−9x2=144 ​

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ 8x2−4y2−16x−3=08 x ^ { 2 } - 4 y ^ { 2 } - 16 x - 3 = 08x2−4y2−16x−3=0 ​

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

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

Identify the equation as a circle,a parabola,an ellipse,or a hyperbola.​ 27x2−18x−200y−119=027 x ^ { 2 } - 18 x - 200 y - 119 = 027x2−18x−200y−119=0 ​

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ 22x2−13x−200y−112=022 x ^ { 2 } - 13 x - 200 y - 112 = 022x2−13x−200y−112=0 ​

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

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

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

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​ Foci: (±10,0)( \pm 10,0 )(±10,0) ;asymptotes: y=±34xy = \pm \frac { 3 } { 4 } xy=±43​x ​

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ x2+y2−7x+2y−12=0x ^ { 2 } + y ^ { 2 } - 7 x + 2 y - 12 = 0x2+y2−7x+2y−12=0 ​

Graph the hyperbola.​ 4x2−16y2=644 x ^ { 2 } - 16 y ^ { 2 } = 644x2−16y2=64 ​

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

Find the center and vertices of the hyperbola. 12x2−4y2−48x+32y−64=012 x ^ { 2 } - 4 y ^ { 2 } - 48 x + 32 y - 64 = 012x2−4y2−48x+32y−64=0

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ 25x2+64y2−14x+17y−119=025 x ^ { 2 } + 64 y ^ { 2 } - 14 x + 17 y - 119 = 025x2+64y2−14x+17y−119=0 ​

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (-10,-2), (0,-2) Asymptotes: y = ± 45\frac { 4 } { 5 }54​ x ​

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Lines

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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