Question 1

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

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 2

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

Accepted Answer

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: $( \pm \sqrt { 5 } , 0 )$ 
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 3

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

Accepted Answer

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: $( \pm \sqrt { 7 } , 0 )$ 
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 4

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

Accepted Answer

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)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 28 } = 64$ 
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 5

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

Accepted Answer

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)  $\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1$ 
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 6

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

Accepted Answer

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) 
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 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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: $( 0 , \pm \sqrt { 49 } )$ 
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 10

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

Accepted Answer

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: $( 0 , \pm \sqrt { 61 } )$ 
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.​ $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$ ​

Accepted Answer

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: $( \pm \sqrt { 41 } , 0 )$ 
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: $( \pm \sqrt { 41 } , 0 )$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

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)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 1 } = 1$ 
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 14

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

Accepted Answer

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: $$y = \pm \frac { 4 } { 3 } x$$ 
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 15

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

Accepted Answer

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) 
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 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

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

Exam 62: Hyperbolas

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ y2−9y−4x−21=0y ^ { 2 } - 9 y - 4 x - 21 = 0y2−9y−4x−21=0 ​

Find the center,vertices and foci of the hyperbola.​ y24−x21=1\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 1 } = 14y2​−1x2​=1 ​

Find the center,vertices and foci of the hyperbola.​ 3x2−4y2=123 x ^ { 2 } - 4 y ^ { 2 } = 123x2−4y2=12 ​

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

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (1,-2), (5,-2) Asymptotes: y=52x,y=−52xy = \frac { 5 } { 2 } x , y = - \frac { 5 } { 2 } xy=25​x,y=−25​x

Find the center and foci of the hyperbola. (y−8)29−(x+5)227=1\frac { ( y - 8 ) ^ { 2 } } { 9 } - \frac { ( x + 5 ) ^ { 2 } } { 27 } = 19(y−8)2​−27(x+5)2​=1

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola.​ (x+5)2121−(y−4)225=1\frac { ( x + 5 ) ^ { 2 } } { 121 } - \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1121(x+5)2​−25(y−4)2​=1 ​

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ x2−6x−3y+8=0x ^ { 2 } - 6 x - 3 y + 8 = 0x2−6x−3y+8=0 ​

Find the center,vertices and foci of the hyperbola.​ 26y2−23x2=59826 y ^ { 2 } - 23 x ^ { 2 } = 59826y2−23x2=598 ​

Find the center,vertices and foci of the hyperbola.​ y225−x236=1\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 125y2​−36x2​=1 ​

Find the center,vertices and foci of the hyperbola.​ x225−y216=1\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 125x2​−16y2​=1 ​

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola.​ (y+3)21/81−(x−2)21/64=1\frac { ( y + 3 ) ^ { 2 } } { 1 / 81 } - \frac { ( x - 2 ) ^ { 2 } } { 1 / 64 } = 11/81(y+3)2​−1/64(x−2)2​=1 ​

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

Find the vertices and asymptotes of the hyperbola. 9y2−16x2=1449 y ^ { 2 } - 16 x ^ { 2 } = 1449y2−16x2=144

Find the center and vertices of the hyperbola. 12x2−4y2−72x−16y+44=012 x ^ { 2 } - 4 y ^ { 2 } - 72 x - 16 y + 44 = 012x2−4y2−72x−16y+44=0

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ y2−4x2+4x−8y−24=0y ^ { 2 } - 4 x ^ { 2 } + 4 x - 8 y - 24 = 0y2−4x2+4x−8y−24=0 ​

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ 2x2−y2+2x+5y−6=02 x ^ { 2 } - y ^ { 2 } + 2 x + 5 y - 6 = 02x2−y2+2x+5y−6=0 ​

Identify the equation as a circle,a parabola,an ellipse,or a hyperbola.​ 16x2+9y2−98x+5y+224=016 x ^ { 2 } + 9 y ^ { 2 } - 98 x + 5 y + 224 = 016x2+9y2−98x+5y+224=0 ​

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ 4x2+3y2+5x−28y+58=04 x ^ { 2 } + 3 y ^ { 2 } + 5 x - 28 y + 58 = 04x2+3y2+5x−28y+58=0 ​

Graph the hyperbola.​ 9y2−16x2+36y+64x=1729 y ^ { 2 } - 16 x ^ { 2 } + 36 y + 64 x = 1729y2−16x2+36y+64x=172 ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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