Question 1

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

Accepted Answer

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: $( \pm \sqrt { 11 } , 0 )$ 
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 2

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

Accepted Answer

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)  $\frac { ( y - 4 ) ^ { 2 } } { 4 } - \frac { ( x + 5 ) ^ { 2 } } { 9 } = 1$ 
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 3

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. )
​

Accepted Answer

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)  $\frac { x ^ { 2 } } { 77,440,000 } + \frac { y ^ { 2 } } { 34,073,600 } = 1$ 
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 4

Select the correct equation of the following graph.​   ​

Accepted Answer

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)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = 1$ 
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 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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: $( \pm \sqrt { 37 } , 0 )$ 
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 12

Select the correct equation of the following graph.​   ​

Accepted Answer

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)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$ 
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 13

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

Accepted Answer

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 
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

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

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: $( \pm \sqrt { 41 } , 0 )$ 
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 16

Select the correct equation of the following graph.​   ​

Accepted Answer

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)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$ 
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 17

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

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 18

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

Accepted Answer

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: $( 0 , \pm \sqrt { 26 } )$ 
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 19

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

Accepted Answer

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)  $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x + 3 ) ^ { 2 } } { 12 } = 1$ 
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 20

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

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

Exam 62: Hyperbolas

Find the center,vertices and foci of the hyperbola.​ 5x2−6y2=305 x ^ { 2 } - 6 y ^ { 2 } = 305x2−6y2=30 ​

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

Select the correct equation of the following graph.​ ​

Graph the hyperbola.​ y225−x225=1\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 25 } = 125y2​−25x2​=1 ​

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola.​ (y−5)21/64−(x+3)21/49=1\frac { ( y - 5 ) ^ { 2 } } { 1 / 64 } - \frac { ( x + 3 ) ^ { 2 } } { 1 / 49 } = 11/64(y−5)2​−1/49(x+3)2​=1 ​

Identify the equation as a circle,a parabola,an ellipse,or a hyperbola.​ 3x2−3y2−3x+6y+17=03 x ^ { 2 } - 3 y ^ { 2 } - 3 x + 6 y + 17 = 03x2−3y2−3x+6y+17=0 ​

Select the correct graph of the following equations of the hyperbola and find the center of hyperbola.​ (x−6)216−(y+2)21=1\frac { ( x - 6 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { 1 } = 116(x−6)2​−1(y+2)2​=1 ​

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ x2+y2−9x+3y−16=0x ^ { 2 } + y ^ { 2 } - 9 x + 3 y - 16 = 0x2+y2−9x+3y−16=0 ​

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ y2+8x+5y+26=0y ^ { 2 } + 8 x + 5 y + 26 = 0y2+8x+5y+26=0 ​

Find the center,vertices and foci of the hyperbola.​ y21−x236=1\frac { y ^ { 2 } } { 1 } - \frac { x ^ { 2 } } { 36 } = 11y2​−36x2​=1 ​

Select the correct equation of the following graph.​ ​

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

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ 9x2+36y2−20x+256y−535=09 x ^ { 2 } + 36 y ^ { 2 } - 20 x + 256 y - 535 = 09x2+36y2−20x+256y−535=0 ​

Find the center,vertices and foci of the hyperbola.​ x216−y225=1\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 116x2​−25y2​=1 ​

Select the correct equation of the following graph.​ ​

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ 100x2+100y2−100x+400y+403=0100 x ^ { 2 } + 100 y ^ { 2 } - 100 x + 400 y + 403 = 0100x2+100y2−100x+400y+403=0 ​

Find the center,vertices and foci of the hyperbola.​ 21x2−5y2=10521 x ^ { 2 } - 5 y ^ { 2 } = 10521x2−5y2=105 ​

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

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ 3y2+3x2−21x+34=03 y ^ { 2 } + 3 x ^ { 2 } - 21 x + 34 = 03y2+3x2−21x+34=0 ​

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

Introduction to Conics Parabolas

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

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

Select the correct equation of the following graph.

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

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

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

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

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

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

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

Select the correct equation of the following graph.

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

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

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

Select the correct equation of the following graph.

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

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

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

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