Question 1

Find the asymptotes of the hyperbola.
-$$x ^ { 2 } - y ^ { 2 } - 6 x + 8 y - 11 = 0$$

Accepted Answer

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

Question 2

Identify the equation without applying a rotation of axes.
-$$10 x ^ { 2 } + 9 x y + 4 y ^ { 2 } + 2 x - 3 y + 5 = 0$$

Accepted Answer

A)  ellipse 
B)  parabola 
C)  hyperbola 
D)  not a conic 
A)  ellipse 
B)  parabola 
C)  hyperbola 
D)  not a conic

Question 3

Convert the polar equation to a rectangular equation.
-$$r = \frac { 4 \sec \theta } { \sec \theta + 2 }$$

Accepted Answer

A)  $3 x ^ { 2 } - y ^ { 2 } - 16 x + 16 = 0$ 
B)  $3 y ^ { 2 } - x ^ { 2 } + 16 = 0$ 
C)  $3 x ^ { 2 } - y ^ { 2 } + 16 = 0$ 
D)  $3 y ^ { 2 } - x ^ { 2 } - 16 y + 16 = 0$ 
A)  $3 x ^ { 2 } - y ^ { 2 } - 16 x + 16 = 0$ 
B)  $3 y ^ { 2 } - x ^ { 2 } + 16 = 0$ 
C)  $3 x ^ { 2 } - y ^ { 2 } + 16 = 0$ 
D)  $3 y ^ { 2 } - x ^ { 2 } - 16 y + 16 = 0$

Question 4

Find parametric equations for the rectangular equation.
-

Accepted Answer

Question 5

Graph the equation.
-$9(x+2)^{2}+4(y-1)^{2}=36$

Accepted Answer

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

Question 6

Find an equation of the parabola described.
-Focus at (0, 21); directrix the line y = -21 A) $x ^ { 2 } = 84 y$

Accepted Answer

B)  $y ^ { 2 } = 84 x$ 
C)  $y ^ { 2 } = 21 x$ 
D)  $x ^ { 2 } = - 84 y$ 
B)  $y ^ { 2 } = 84 x$ 
C)  $y ^ { 2 } = 21 x$ 
D)  $x ^ { 2 } = - 84 y$

Question 7

Find an equation for the ellipse described.
-Foci at $( \pm 2,0 ) ; \quad x$-intercepts are $\pm 7$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 45 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 45 } = 1$ 
A)  $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 45 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 45 } = 1$

Question 8

Find the vertex, focus, and directrix of the parabola.
-$x^{2}=-8 y$
 
 A) vertex: $( 0,0 )$
focus: $( 0,2 )$
directrix: $y = - 2$

Accepted Answer

B)  vertex: $( 0,0 )$
focus: $( - 2,0 )$
directrix: $x = 2$

C)  vertex: $( 0,0 )$
focus: $( 0 , - 2 )$
directrix: $y = 2$

D)  vertex: $( 0,0 )$
focus: $( 2,0 )$
directrix: $x = - 2$
  
B)  vertex: $( 0,0 )$
focus: $( - 2,0 )$
directrix: $x = 2$

C)  vertex: $( 0,0 )$
focus: $( 0 , - 2 )$
directrix: $y = 2$

D)  vertex: $( 0,0 )$
focus: $( 2,0 )$
directrix: $x = - 2$

Question 9

Match the equation to the graph.
-$$( y + 2 ) ^ { 2 } = - 7 ( x - 1 )$$

Accepted Answer

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

Question 10

Find an equation for the ellipse described.
-Foci at $( 0 , \pm 5 ) ; \quad \mathrm { y }$-intercepts are $\pm 8$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 39 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 39 } = 1$ 
D)  $\frac { x ^ { 2 } } { 39 } + \frac { y ^ { 2 } } { 64 } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 39 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 39 } = 1$ 
D)  $\frac { x ^ { 2 } } { 39 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 11

Find an equation for the hyperbola described.
-Vertices at $( 0 , \pm 10 )$; asymptotes at $y = \pm \frac { 5 } { 3 } x$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 36 } = 1$ 
B)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
C)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 100 } = 1$ 
D)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 9 } = 1$ 5 
A)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 36 } = 1$ 
B)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
C)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 100 } = 1$ 
D)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 9 } = 1$ 5

Question 12

Find the center, foci, and vertices of the ellipse.
-$$\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$$

Accepted Answer

A)  center at $( 0,0 )$
foci at $( 0,8 )$ and $( 4,0 )$
vertices at $( 0,64 ) , ( 16,0 )$ 
B)  center at $( 0,0 )$
foci at $( 0 , - 8 )$ and $( 0,8 )$
vertices at $( 0 , - 64 ) , ( 0,64 )$ 
C)  center at $( 0,0 )$
foci at $( - 4 \sqrt { 3 } , 0 )$ and $( 4 \sqrt { 3 } , 0 )$
vertices at $( - 8,0 ) , ( 8,0 )$ 
D)  center at $( 0,0 )$
foci at $( 0 , - 4 \sqrt { 3 } )$ and $( 0,4 \sqrt { 3 } )$
vertices at $( 0 , - 8 ) , ( 0,8 )$ 
A)  center at $( 0,0 )$
foci at $( 0,8 )$ and $( 4,0 )$
vertices at $( 0,64 ) , ( 16,0 )$ 
B)  center at $( 0,0 )$
foci at $( 0 , - 8 )$ and $( 0,8 )$
vertices at $( 0 , - 64 ) , ( 0,64 )$ 
C)  center at $( 0,0 )$
foci at $( - 4 \sqrt { 3 } , 0 )$ and $( 4 \sqrt { 3 } , 0 )$
vertices at $( - 8,0 ) , ( 8,0 )$ 
D)  center at $( 0,0 )$
foci at $( 0 , - 4 \sqrt { 3 } )$ and $( 0,4 \sqrt { 3 } )$
vertices at $( 0 , - 8 ) , ( 0,8 )$

Question 13

Find an equation for the hyperbola described.
-Vertices $\left( \frac { 1 } { 2 } , - 3 \right)$ and $\left( - \frac { 9 } { 2 } , - 3 \right) ;$ asymptotes $\mathrm { y } + 3 = \pm \frac { 6 } { 5 } ( \mathrm { x } + 2 )$

Accepted Answer

A)  $\frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { 4 ( y + 3 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { 4 ( \mathrm { x } + 2 ) ^ { 2 } } { 25 } - \frac { ( \mathrm { y } + 3 ) ^ { 2 } } { 9 } = 1$ 
C)  $\frac { ( y + 3 ) ^ { 2 } } { 9 } - \frac { 4 ( x + 2 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { 4 ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$ 
A)  $\frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { 4 ( y + 3 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { 4 ( \mathrm { x } + 2 ) ^ { 2 } } { 25 } - \frac { ( \mathrm { y } + 3 ) ^ { 2 } } { 9 } = 1$ 
C)  $\frac { ( y + 3 ) ^ { 2 } } { 9 } - \frac { 4 ( x + 2 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { 4 ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$

Question 14

Graph the equation.
-$$\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$$

Accepted Answer

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

Question 15

Find an equation for the hyperbola described. Graph the equation.
-Center at $( 0,0 ) ;$ vertex at $( 0,3 ) ;$ focus at $( 0 , \sqrt { 13 } )$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$
  
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1$
  
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$
  
D)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$
  
A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$
  
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1$
  
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$
  
D)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$

Question 16

Find an equation for the ellipse described.
-Center at $( 6,4 )$; focus at $( 10,4 )$; vertex at $( 12,4 )$

Accepted Answer

A)  $\frac { ( x + 6 ) ^ { 2 } } { 36 } + \frac { ( y + 4 ) ^ { 2 } } { 20 } = 1$ 
B)  $\frac { ( x - 6 ) ^ { 2 } } { 81 } + \frac { ( y + 4 ) ^ { 2 } } { 8 } = 2$ 
C)  $\frac { ( x + 6 ) ^ { 2 } } { 16 } - \frac { ( y - 4 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x - 6 ) ^ { 2 } } { 36 } + \frac { ( y - 4 ) ^ { 2 } } { 20 } = 1$ 
A)  $\frac { ( x + 6 ) ^ { 2 } } { 36 } + \frac { ( y + 4 ) ^ { 2 } } { 20 } = 1$ 
B)  $\frac { ( x - 6 ) ^ { 2 } } { 81 } + \frac { ( y + 4 ) ^ { 2 } } { 8 } = 2$ 
C)  $\frac { ( x + 6 ) ^ { 2 } } { 16 } - \frac { ( y - 4 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x - 6 ) ^ { 2 } } { 36 } + \frac { ( y - 4 ) ^ { 2 } } { 20 } = 1$

Question 17

Identify the equation without applying a rotation of axes.
-$$x ^ { 2 } - 3 x y - 3 y ^ { 2 } - 2 x - 3 y - 5 = 0$$

Accepted Answer

A)  parabola 
B)  ellipse 
C)  hyperbola 
D)  not a conic 
A)  parabola 
B)  ellipse 
C)  hyperbola 
D)  not a conic

Question 18

Graph the hyperbola.
-A satellite following the hyperbolic path shown in the picture turns rapidly at $( 0,4 )$ and then moves closer and closer to the line $y = \frac { 8 } { 5 } \times$ as it gets farther from the tracking station at the origin. Find the equation that describes the path of the rocket if the center of the hyperbola is at $( 0,0 )$.

Accepted Answer

A)  $\frac { y ^ { 2 } } { \frac { 25 } { 4 } } - \frac { x ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { \left( \frac { 12 } { 5 } \right) ^ { 2 } } - \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { \left( \frac { 16 } { 5 } \right) ^ { 2 } } = 1$ 
D)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { \frac { 25 } { 4 } } = 1$ 
A)  $\frac { y ^ { 2 } } { \frac { 25 } { 4 } } - \frac { x ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { \left( \frac { 12 } { 5 } \right) ^ { 2 } } - \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { \left( \frac { 16 } { 5 } \right) ^ { 2 } } = 1$ 
D)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { \frac { 25 } { 4 } } = 1$

Question 19

Write an equation for the hyperbola.
-

Accepted Answer

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

Question 20

Solve the problem.
-Find parametric equations for an object that moves along the ellipse $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 81 } = 1$ with the motion described.
The motion begins at $( 3,0 )$, is counterclockwise, and requires 5 seconds for a complete revolution.

Accepted Answer

A)  $x = 3 \cos \left( \frac { 2 \pi } { 5 } t \right) , y = - 9 \sin \left( \frac { 2 \pi } { 5 } t \right) , 0 \leq t \leq 5$ 
B)  $x = - 4 \cos \left( \frac { 2 \pi } { 3 } t \right) , y = 6 \sin \left( \frac { 2 \pi } { 3 } t \right) , 0 \leq t \leq 3$ 
C)  $x = - 3 \cos \left( \frac { 2 \pi } { 5 } t \right) , y = - 9 \sin \left( \frac { 2 \pi } { 5 } t \right) , 0 \leq t \leq 5$ 
D)  $x = 4 \cos \left( \frac { 2 \pi } { 3 } t \right) , y = 6 \sin \left( \frac { 2 \pi } { 3 } t \right) , 0 \leq t \leq 3$ 
A)  $x = 3 \cos \left( \frac { 2 \pi } { 5 } t \right) , y = - 9 \sin \left( \frac { 2 \pi } { 5 } t \right) , 0 \leq t \leq 5$ 
B)  $x = - 4 \cos \left( \frac { 2 \pi } { 3 } t \right) , y = 6 \sin \left( \frac { 2 \pi } { 3 } t \right) , 0 \leq t \leq 3$ 
C)  $x = - 3 \cos \left( \frac { 2 \pi } { 5 } t \right) , y = - 9 \sin \left( \frac { 2 \pi } { 5 } t \right) , 0 \leq t \leq 5$ 
D)  $x = 4 \cos \left( \frac { 2 \pi } { 3 } t \right) , y = 6 \sin \left( \frac { 2 \pi } { 3 } t \right) , 0 \leq t \leq 3$

Find the asymptotes of the hyperbola. - $x ^ { 2 } - y ^ { 2 } - 6 x + 8 y - 11 = 0$

Identify the equation without applying a rotation of axes. - $10 x ^ { 2 } + 9 x y + 4 y ^ { 2 } + 2 x - 3 y + 5 = 0$

Convert the polar equation to a rectangular equation. - $r = \frac { 4 \sec \theta } { \sec \theta + 2 }$

Find parametric equations for the rectangular equation. -

Graph the equation. - $9(x+2)^{2}+4(y-1)^{2}=36$ $Graph the equation. - 9(x+2)^{2}+4(y-1)^{2}=36$

Find an equation of the parabola described. -Focus at (0, 21); directrix the line y = -21 A) $x ^ { 2 } = 84 y$ B) $y ^ { 2 } = 84 x$ C) $y ^ { 2 } = 21 x$ D) $x ^ { 2 } = - 84 y$

Find an equation for the ellipse described. -Foci at $( \pm 2,0 ) ; \quad x$ -intercepts are $\pm 7$

Match the equation to the graph. - $( y + 2 ) ^ { 2 } = - 7 ( x - 1 )$

Find an equation for the ellipse described. -Foci at $( 0 , \pm 5 ) ; \quad \mathrm { y }$ -intercepts are $\pm 8$

Find an equation for the hyperbola described. -Vertices at $( 0 , \pm 10 )$ ; asymptotes at $y = \pm \frac { 5 } { 3 } x$

Find the center, foci, and vertices of the ellipse. - $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$

Find an equation for the hyperbola described. -Vertices $\left( \frac { 1 } { 2 } , - 3 \right)$ and $\left( - \frac { 9 } { 2 } , - 3 \right) ;$ asymptotes $\mathrm { y } + 3 = \pm \frac { 6 } { 5 } ( \mathrm { x } + 2 )$

Graph the equation. - $\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$ $Graph the equation. - \frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$

Find an equation for the hyperbola described. Graph the equation. -Center at $( 0,0 ) ;$ vertex at $( 0,3 ) ;$ focus at $( 0 , \sqrt { 13 } )$ $Find an equation for the hyperbola described. Graph the equation. -Center at ( 0,0 ) ; vertex at ( 0,3 ) ; focus at ( 0 , \sqrt { 13 } )$

Find an equation for the ellipse described. -Center at $( 6,4 )$ ; focus at $( 10,4 )$ ; vertex at $( 12,4 )$

Identify the equation without applying a rotation of axes. - $x ^ { 2 } - 3 x y - 3 y ^ { 2 } - 2 x - 3 y - 5 = 0$

Write an equation for the hyperbola. -

Solve the problem. -Find parametric equations for an object that moves along the ellipse $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 81 } = 1$ with the motion described. The motion begins at $( 3,0 )$ , is counterclockwise, and requires 5 seconds for a complete revolution.

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 9: Analytic Geometry

Find the asymptotes of the hyperbola. - x2−y2−6x+8y−11=0x ^ { 2 } - y ^ { 2 } - 6 x + 8 y - 11 = 0x2−y2−6x+8y−11=0

Identify the equation without applying a rotation of axes. - 10x2+9xy+4y2+2x−3y+5=010 x ^ { 2 } + 9 x y + 4 y ^ { 2 } + 2 x - 3 y + 5 = 010x2+9xy+4y2+2x−3y+5=0

Convert the polar equation to a rectangular equation. - r=4sec⁡θsec⁡θ+2r = \frac { 4 \sec \theta } { \sec \theta + 2 }r=secθ+24secθ​

Find parametric equations for the rectangular equation. -

Graph the equation. - 9(x+2)2+4(y−1)2=369(x+2)^{2}+4(y-1)^{2}=369(x+2)2+4(y−1)2=36

Find an equation of the parabola described. -Focus at (0, 21); directrix the line y = -21 A) x2=84yx ^ { 2 } = 84 yx2=84y B) y2=84xy ^ { 2 } = 84 xy2=84x C) y2=21xy ^ { 2 } = 21 xy2=21x D) x2=−84yx ^ { 2 } = - 84 yx2=−84y

Find an equation for the ellipse described. -Foci at (±2,0);x( \pm 2,0 ) ; \quad x(±2,0);x -intercepts are ±7\pm 7±7

Match the equation to the graph. - (y+2)2=−7(x−1)( y + 2 ) ^ { 2 } = - 7 ( x - 1 )(y+2)2=−7(x−1)

Find an equation for the ellipse described. -Foci at (0,±5);y( 0 , \pm 5 ) ; \quad \mathrm { y }(0,±5);y -intercepts are ±8\pm 8±8

Find an equation for the hyperbola described. -Vertices at (0,±10)( 0 , \pm 10 )(0,±10) ; asymptotes at y=±53xy = \pm \frac { 5 } { 3 } xy=±35​x

Find the center, foci, and vertices of the ellipse. - x216+y264=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 116x2​+64y2​=1

Find an equation for the hyperbola described. -Vertices (12,−3)\left( \frac { 1 } { 2 } , - 3 \right)(21​,−3) and (−92,−3);\left( - \frac { 9 } { 2 } , - 3 \right) ;(−29​,−3); asymptotes y+3=±65(x+2)\mathrm { y } + 3 = \pm \frac { 6 } { 5 } ( \mathrm { x } + 2 )y+3=±56​(x+2)

Graph the equation. - (x−1)29+(y+1)24=1\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 19(x−1)2​+4(y+1)2​=1

Find an equation for the hyperbola described. Graph the equation. -Center at (0,0);( 0,0 ) ;(0,0); vertex at (0,3);( 0,3 ) ;(0,3); focus at (0,13)( 0 , \sqrt { 13 } )(0,13​)

Find an equation for the ellipse described. -Center at (6,4)( 6,4 )(6,4) ; focus at (10,4)( 10,4 )(10,4) ; vertex at (12,4)( 12,4 )(12,4)

Identify the equation without applying a rotation of axes. - x2−3xy−3y2−2x−3y−5=0x ^ { 2 } - 3 x y - 3 y ^ { 2 } - 2 x - 3 y - 5 = 0x2−3xy−3y2−2x−3y−5=0

Write an equation for the hyperbola. -

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Find the asymptotes of the hyperbola. - $x ^ { 2 } - y ^ { 2 } - 6 x + 8 y - 11 = 0$

Identify the equation without applying a rotation of axes. - $10 x ^ { 2 } + 9 x y + 4 y ^ { 2 } + 2 x - 3 y + 5 = 0$

Convert the polar equation to a rectangular equation. - $r = \frac { 4 \sec \theta } { \sec \theta + 2 }$

Graph the equation. - $9(x+2)^{2}+4(y-1)^{2}=36$ $Graph the equation. - 9(x+2)^{2}+4(y-1)^{2}=36$

Find an equation of the parabola described. -Focus at (0, 21); directrix the line y = -21 A) $x ^ { 2 } = 84 y$ B) $y ^ { 2 } = 84 x$ C) $y ^ { 2 } = 21 x$ D) $x ^ { 2 } = - 84 y$

Find an equation for the ellipse described. -Foci at $( \pm 2,0 ) ; \quad x$ -intercepts are $\pm 7$

Match the equation to the graph. - $( y + 2 ) ^ { 2 } = - 7 ( x - 1 )$

Find an equation for the ellipse described. -Foci at $( 0 , \pm 5 ) ; \quad \mathrm { y }$ -intercepts are $\pm 8$

Find an equation for the hyperbola described. -Vertices at $( 0 , \pm 10 )$ ; asymptotes at $y = \pm \frac { 5 } { 3 } x$

Find the center, foci, and vertices of the ellipse. - $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$

Find an equation for the hyperbola described. -Vertices $\left( \frac { 1 } { 2 } , - 3 \right)$ and $\left( - \frac { 9 } { 2 } , - 3 \right) ;$ asymptotes $\mathrm { y } + 3 = \pm \frac { 6 } { 5 } ( \mathrm { x } + 2 )$

Graph the equation. - $\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$ $Graph the equation. - \frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$

Find an equation for the hyperbola described. Graph the equation. -Center at $( 0,0 ) ;$ vertex at $( 0,3 ) ;$ focus at $( 0 , \sqrt { 13 } )$ $Find an equation for the hyperbola described. Graph the equation. -Center at ( 0,0 ) ; vertex at ( 0,3 ) ; focus at ( 0 , \sqrt { 13 } )$

Find an equation for the ellipse described. -Center at $( 6,4 )$ ; focus at $( 10,4 )$ ; vertex at $( 12,4 )$

Identify the equation without applying a rotation of axes. - $x ^ { 2 } - 3 x y - 3 y ^ { 2 } - 2 x - 3 y - 5 = 0$