Question 1

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
-$$\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$$

Accepted Answer

A)  center at $( 0,0 )$
transverse axis is $x$-axis
vertices at $( - 11,0 )$ and $( 11,0 )$
foci at $( - \sqrt { 137 } , 0 )$ and $( \sqrt { 137 } , 0 )$
asymptotes of $y = - \frac { 11 } { 4 }$ and $y = \frac { 11 } { 4 }$ 
B)  center at $( 0,0 )$
transverse axis is $\mathrm { y }$-axis
vertices at $( 0 , - 4 )$ and $( 0,4 )$
foci at $( - \sqrt { 137 } , 0 )$ and $( \sqrt { 137 } , 0 )$
asymptotes of $y = - \frac { 11 } { 4 }$ and $y = \frac { 11 } { 4 }$ 
C)  center at $( 0,0 )$
transverse axis is $\mathrm { x }$-axis
vertices at $( - 4,0 )$ and $( 4,0 )$
foci at $( - 11,0 )$ and $( 11,0 )$
asymptotes of $y = - \frac { 11 } { 4 }$ and $y = \frac { 11 } { 4 }$ 
D)  center at $( 0,0 )$
transverse axis is $x$-axis
vertices at $( - 4,0 )$ and $( 4,0 )$
foci at $( - \sqrt { 137 } , 0 )$ and $( \sqrt { 137 } , 0 )$
asymptotes of $y = - \frac { 11 } { 4 }$ and $y = \frac { 11 } { 4 }$ 
A)  center at $( 0,0 )$
transverse axis is $x$-axis
vertices at $( - 11,0 )$ and $( 11,0 )$
foci at $( - \sqrt { 137 } , 0 )$ and $( \sqrt { 137 } , 0 )$
asymptotes of $y = - \frac { 11 } { 4 }$ and $y = \frac { 11 } { 4 }$ 
B)  center at $( 0,0 )$
transverse axis is $\mathrm { y }$-axis
vertices at $( 0 , - 4 )$ and $( 0,4 )$
foci at $( - \sqrt { 137 } , 0 )$ and $( \sqrt { 137 } , 0 )$
asymptotes of $y = - \frac { 11 } { 4 }$ and $y = \frac { 11 } { 4 }$ 
C)  center at $( 0,0 )$
transverse axis is $\mathrm { x }$-axis
vertices at $( - 4,0 )$ and $( 4,0 )$
foci at $( - 11,0 )$ and $( 11,0 )$
asymptotes of $y = - \frac { 11 } { 4 }$ and $y = \frac { 11 } { 4 }$ 
D)  center at $( 0,0 )$
transverse axis is $x$-axis
vertices at $( - 4,0 )$ and $( 4,0 )$
foci at $( - \sqrt { 137 } , 0 )$ and $( \sqrt { 137 } , 0 )$
asymptotes of $y = - \frac { 11 } { 4 }$ and $y = \frac { 11 } { 4 }$ D

Question 2

Match the equation to the graph.
-  A) $x ^ { 2 } = 4 y$

Accepted Answer

B)  $x ^ { 2 } = - 4 y$ 
C)  $y ^ { 2 } = 4 x$ 
D)  $y ^ { 2 } = - 4 x$ 
B)  $x ^ { 2 } = - 4 y$ 
C)  $y ^ { 2 } = 4 x$ 
D)  $y ^ { 2 } = - 4 x$ C

Question 3

Find an equation for the hyperbola described.
-Vertices at $( \pm 2,0 )$; foci at $( \pm 11,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 117 } = 1$ 
C)  $\frac { x ^ { 2 } } { 117 } - \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 121 } = 1$ 
A)  $\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 117 } = 1$ 
C)  $\frac { x ^ { 2 } } { 117 } - \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 121 } = 1$ B

Question 4

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati
-$x^{2}+2 x y+y^{2}-8 x+8 y=0$

Accepted Answer

A) 
$\begin{array}{l}
\theta=36.9^{\circ} \
\frac{x^{\prime 2}}{4}+\frac{y^{\prime 2}}{4}=1 \
\text { ellipse } \
\text { center }(0,0) \
\text { major axis is } x^{\prime} \text {-axi: } \
\text { vertices at }(\pm 2,0)
\end{array}$ 
B) 
$\begin{array}{l}
\theta=36.9^{\circ} \
\frac{x^{2}}{4}+\frac{y^{2}}{2}=1 \
\text { ellipse } \
\text { center }(0,0) \
\text { major axis is } x^{\prime} \text {-axi: } \
\text { vertices at }(\pm 2,0)
\end{array}$ 
C) 
$\begin{array}{l}
\theta=45^{\circ} \
x^{\prime 2}=-4 \sqrt{2} y^{\prime} \
\text { parabola } \
\text { vertex at }(0,0) \
\text { focus at }(0,-\sqrt{2})
\end{array}$ 
D) 
$\begin{array}{l}
\theta=45^{\circ} \
y^{\prime 2}=-4 \sqrt{2} x^{\prime} \
\text { parabola } \
\text { vertex at }(0,0) \
\text { focus at }(-\sqrt{2}, 0)
\end{array}$ 
A) 
$\begin{array}{l}
\theta=36.9^{\circ} \
\frac{x^{\prime 2}}{4}+\frac{y^{\prime 2}}{4}=1 \
\text { ellipse } \
\text { center }(0,0) \
\text { major axis is } x^{\prime} \text {-axi: } \
\text { vertices at }(\pm 2,0)
\end{array}$ 
B) 
$\begin{array}{l}
\theta=36.9^{\circ} \
\frac{x^{2}}{4}+\frac{y^{2}}{2}=1 \
\text { ellipse } \
\text { center }(0,0) \
\text { major axis is } x^{\prime} \text {-axi: } \
\text { vertices at }(\pm 2,0)
\end{array}$ 
C) 
$\begin{array}{l}
\theta=45^{\circ} \
x^{\prime 2}=-4 \sqrt{2} y^{\prime} \
\text { parabola } \
\text { vertex at }(0,0) \
\text { focus at }(0,-\sqrt{2})
\end{array}$ 
D) 
$\begin{array}{l}
\theta=45^{\circ} \
y^{\prime 2}=-4 \sqrt{2} x^{\prime} \
\text { parabola } \
\text { vertex at }(0,0) \
\text { focus at }(-\sqrt{2}, 0)
\end{array}$

Question 5

Match the equation to its graph.
-$$y ^ { 2 } = - 10 x$$

Accepted Answer

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

Question 6

Find an equation for the parabola described.
-Vertex at (7, -9); focus at (3, -9) A) $( x + 8 ) ^ { 2 } = - 4 ( y - 4 )$

Accepted Answer

B)  $( x + 8 ) ^ { 2 } = 4 ( y - 4 )$ 
C)  $( y + 4 ) ^ { 2 } = - 12 ( x - 8 )$ 
D)  $( y + 9 ) ^ { 2 } = 16 ( x - 7 )$ 
B)  $( x + 8 ) ^ { 2 } = 4 ( y - 4 )$ 
C)  $( y + 4 ) ^ { 2 } = - 12 ( x - 8 )$ 
D)  $( y + 9 ) ^ { 2 } = 16 ( x - 7 )$

Question 7

Write an equation for the graph.
-

Accepted Answer

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

Question 8

Match the equation to its graph.
-$x ^ { 2 } = 7 y$

Accepted Answer

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

Question 9

Find a rectangular equation for the plane curve defined by the parametric equations.
-A baseball pitcher throws a baseball with an initial speed of 140 feet per second at an angle of 20° to the horizontal. The ball leaves the pitcher's hand at a height of 5 feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height?
What is the maximum height of the ball? A) $x = 124.04 t$ and $y = - 16 t ^ { 2 } + 45.14 t + 5$
$5.856 \mathrm { sec } , 1.411 \mathrm { sec }$,
$31.838$ feet

Accepted Answer

B)  $x = 124.04 t$ and $y = - 16 t ^ { 2 } + 45.14 t + 5$
$5.412 \mathrm { sec } , 1.411 \mathrm { sec }$,
$259.702$ feet 
C)  $x = 124.04 t$ and $y = - 16 t ^ { 2 } + 45.14 t + 5$
$2.706 \mathrm { sec } , 1.411 \mathrm { sec }$,
$4.99$ feet 
D)  $x = 131.56 \mathrm { t }$ and $\mathrm { y } = - 16 \mathrm { t } ^ { 2 } + 47.88 \mathrm { t } + 5$
$3.094 \mathrm { sec } , 1.496 \mathrm { sec }$,
$40.82$ feet 
B)  $x = 124.04 t$ and $y = - 16 t ^ { 2 } + 45.14 t + 5$
$5.412 \mathrm { sec } , 1.411 \mathrm { sec }$,
$259.702$ feet 
C)  $x = 124.04 t$ and $y = - 16 t ^ { 2 } + 45.14 t + 5$
$2.706 \mathrm { sec } , 1.411 \mathrm { sec }$,
$4.99$ feet 
D)  $x = 131.56 \mathrm { t }$ and $\mathrm { y } = - 16 \mathrm { t } ^ { 2 } + 47.88 \mathrm { t } + 5$
$3.094 \mathrm { sec } , 1.496 \mathrm { sec }$,
$40.82$ feet

Question 10

Graph the hyperbola.
-$(x-2)^{2}-4(y-2)^{2}=4$

Accepted Answer

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

Question 11

Graph the hyperbola.
-$\frac{(x-2)^{2}}{4}-\frac{(y-2)^{2}}{16}=1$

Accepted Answer

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

Question 12

Identify the conic that the polar equation represents. Also, give the position of the directrix.
-$$r = \frac { 6 } { 3 - 4 \cos \theta }$$

Accepted Answer

A)  ellipse, directrix is perpendicular to the polar axis at a distance $\frac { 3 } { 2 }$ units to the right of the pole 
B)  hyperbola, directrix is perpendicular to the polar axis at a distance 3 units to the right of the pole 
C)  hyperbola, directrix is perpendicular to the polar axis at a distance $\frac { 3 } { 2 }$ units to the left of the pole 
D)  ellipse, directrix is perpendicular to the polar axis at a distance 3 units to the left of the pole 
A)  ellipse, directrix is perpendicular to the polar axis at a distance $\frac { 3 } { 2 }$ units to the right of the pole 
B)  hyperbola, directrix is perpendicular to the polar axis at a distance 3 units to the right of the pole 
C)  hyperbola, directrix is perpendicular to the polar axis at a distance $\frac { 3 } { 2 }$ units to the left of the pole 
D)  ellipse, directrix is perpendicular to the polar axis at a distance 3 units to the left of the pole

Question 13

Graph the hyperbola.
-The roof of a building is in the shape of the hyperbola $y ^ { 2 } - x ^ { 2 } = 33$, where $x$ and $y$ are in meters. Refer to the figure and determine the height $h$ of the outside walls.

$$a = b = 7 m$$

Accepted Answer

A)  37 m 
B)  35 m 
C)  125 m 
D)  11.2 m 
A)  37 m 
B)  35 m 
C)  125 m 
D)  11.2 m

Question 14

Graph the curve whose parametric equations are given.
-$x=2 t^{2}$ , $y=t+2$ : $- \infty < t < \infty$

A)

Accepted Answer

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

Question 15

Find the center, foci, and vertices of the ellipse.
-$$4 x ^ { 2 } + 64 y ^ { 2 } = 256$$

Accepted Answer

A)  center at $( 0,0 )$
foci at $( 0 , - 2 )$ and $( 0,2 )$
vertices at $( 0 , - 4 ) , ( 0,4 )$ 
B)  center at $( 0,0 )$
foci at $( 0 , - 2 \sqrt { 15 } )$ and $( 0,2 \sqrt { 15 } )$
vertices at $( 0 , - 8 ) , ( 0,8 )$ 
C)  center at $( 0,0 )$
foci at $( - 2 \sqrt { 15 } , 0 )$ and $( 2 \sqrt { 15 } , 0 )$
vertices at $( - 8,0 ) , ( 8,0 )$ 
D)  center at $( 0,0 )$
foci at $( - 8,0 )$ and $( 8,0 )$
vertices at $( - 64,0 ) , ( 64,0 )$ 
A)  center at $( 0,0 )$
foci at $( 0 , - 2 )$ and $( 0,2 )$
vertices at $( 0 , - 4 ) , ( 0,4 )$ 
B)  center at $( 0,0 )$
foci at $( 0 , - 2 \sqrt { 15 } )$ and $( 0,2 \sqrt { 15 } )$
vertices at $( 0 , - 8 ) , ( 0,8 )$ 
C)  center at $( 0,0 )$
foci at $( - 2 \sqrt { 15 } , 0 )$ and $( 2 \sqrt { 15 } , 0 )$
vertices at $( - 8,0 ) , ( 8,0 )$ 
D)  center at $( 0,0 )$
foci at $( - 8,0 )$ and $( 8,0 )$
vertices at $( - 64,0 ) , ( 64,0 )$

Question 16

Find an equation for the ellipse described.
-Center at $( 0,0 )$; focus at $( - 5,0 ) ;$ vertex at $( 8,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 60 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 60 } = 1$ 
D)  $\frac { x ^ { 2 } } { 60 } + \frac { y ^ { 2 } } { 64 } = 1$ 
A)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 60 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 60 } = 1$ 
D)  $\frac { x ^ { 2 } } { 60 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 17

Match the equation to its graph.
-$$x ^ { 2 } = - 12 y$$

Accepted Answer

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

Question 18

Discuss the equation and graph it.
-$r=\frac{6}{3-3 \cos \theta}$

Accepted Answer

A)  directrix perpendicular to polar
axis 2 left of pole
focus $( 0,0 )$, vertex $( 1 , \pi )$ 
  
B)  directrix perpendicular to polar  
axis 2 right of pole 
focus $( 0,0 )$, vertex $( 1,0 )$

C)  directrix parallel to polar
 axis 2 below pole
focus $( 0,0 )$, vertex $\left( 1 , \frac { 3 \pi } { 2 } \right)$

D)  directrix parallel to polar 
axis 2 above pole 
focus $( 0,0 )$, vertex $\left( 1 , \frac {  \pi } { 2 } \right)$
  
A)  directrix perpendicular to polar
axis 2 left of pole
focus $( 0,0 )$, vertex $( 1 , \pi )$ 
  
B)  directrix perpendicular to polar  
axis 2 right of pole 
focus $( 0,0 )$, vertex $( 1,0 )$

C)  directrix parallel to polar
 axis 2 below pole
focus $( 0,0 )$, vertex $\left( 1 , \frac { 3 \pi } { 2 } \right)$

D)  directrix parallel to polar 
axis 2 above pole 
focus $( 0,0 )$, vertex $\left( 1 , \frac {  \pi } { 2 } \right)$

Question 19

Graph the hyperbola.
-$\frac{x^{2}}{4}-\frac{y^{2}}{36}=1$

Accepted Answer

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

Question 20

Identify the conic that the polar equation represents. Also, give the position of the directrix.
-$$r = \frac { 2 } { 1 - 2 \cos \theta }$$

Accepted Answer

A)  hyperbola, directrix perpendicular to the polar axis 1 right of the pole 
B)  ellipse, directrix perpendicular to the polar axis 1 right of the pole 
C)  ellipse, directrix perpendicular to the polar axis 1 left of the pole 
D)  hyperbola, directrix perpendicular to the polar axis 1 left of the pole 
A)  hyperbola, directrix perpendicular to the polar axis 1 right of the pole 
B)  ellipse, directrix perpendicular to the polar axis 1 right of the pole 
C)  ellipse, directrix perpendicular to the polar axis 1 left of the pole 
D)  hyperbola, directrix perpendicular to the polar axis 1 left of the pole

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$

Match the equation to the graph. - $Match the equation to the graph. - A) x ^ { 2 } = 4 y B) x ^ { 2 } = - 4 y C) y ^ { 2 } = 4 x D) y ^ { 2 } = - 4 x$ A) $x ^ { 2 } = 4 y$ B) $x ^ { 2 } = - 4 y$ C) $y ^ { 2 } = 4 x$ D) $y ^ { 2 } = - 4 x$

Find an equation for the hyperbola described. -Vertices at $( \pm 2,0 )$ ; foci at $( \pm 11,0 )$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati - $x^{2}+2 x y+y^{2}-8 x+8 y=0$

Match the equation to its graph. - $y ^ { 2 } = - 10 x$

Find an equation for the parabola described. -Vertex at (7, -9); focus at (3, -9) A) $( x + 8 ) ^ { 2 } = - 4 ( y - 4 )$ B) $( x + 8 ) ^ { 2 } = 4 ( y - 4 )$ C) $( y + 4 ) ^ { 2 } = - 12 ( x - 8 )$ D) $( y + 9 ) ^ { 2 } = 16 ( x - 7 )$

Write an equation for the graph. -

Match the equation to its graph. - $x ^ { 2 } = 7 y$

Graph the hyperbola. - $(x-2)^{2}-4(y-2)^{2}=4$ $Graph the hyperbola. - (x-2)^{2}-4(y-2)^{2}=4$

Graph the hyperbola. - $\frac{(x-2)^{2}}{4}-\frac{(y-2)^{2}}{16}=1$ $Graph the hyperbola. - \frac{(x-2)^{2}}{4}-\frac{(y-2)^{2}}{16}=1$

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 6 } { 3 - 4 \cos \theta }$

Find the center, foci, and vertices of the ellipse. - $4 x ^ { 2 } + 64 y ^ { 2 } = 256$

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( - 5,0 ) ;$ vertex at $( 8,0 )$

Match the equation to its graph. - $x ^ { 2 } = - 12 y$

Discuss the equation and graph it. - $r=\frac{6}{3-3 \cos \theta}$ $Discuss the equation and graph it. - r=\frac{6}{3-3 \cos \theta}$

Graph the hyperbola. - $\frac{x^{2}}{4}-\frac{y^{2}}{36}=1$ $Graph the hyperbola. - \frac{x^{2}}{4}-\frac{y^{2}}{36}=1$

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 2 } { 1 - 2 \cos \theta }$

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 center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - x236−y24=1\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 136x2​−4y2​=1

Match the equation to the graph. - A) x2=4yx ^ { 2 } = 4 yx2=4y B) x2=−4yx ^ { 2 } = - 4 yx2=−4y C) y2=4xy ^ { 2 } = 4 xy2=4x D) y2=−4xy ^ { 2 } = - 4 xy2=−4x

Find an equation for the hyperbola described. -Vertices at (±2,0)( \pm 2,0 )(±2,0) ; foci at (±11,0)( \pm 11,0 )(±11,0)

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati - x2+2xy+y2−8x+8y=0x^{2}+2 x y+y^{2}-8 x+8 y=0x2+2xy+y2−8x+8y=0

Match the equation to its graph. - y2=−10xy ^ { 2 } = - 10 xy2=−10x

Write an equation for the graph. -

Match the equation to its graph. - x2=7yx ^ { 2 } = 7 yx2=7y

Graph the hyperbola. - (x−2)2−4(y−2)2=4(x-2)^{2}-4(y-2)^{2}=4(x−2)2−4(y−2)2=4

Graph the hyperbola. - (x−2)24−(y−2)216=1\frac{(x-2)^{2}}{4}-\frac{(y-2)^{2}}{16}=14(x−2)2​−16(y−2)2​=1

Identify the conic that the polar equation represents. Also, give the position of the directrix. - r=63−4cos⁡θr = \frac { 6 } { 3 - 4 \cos \theta }r=3−4cosθ6​

Graph the hyperbola. -The roof of a building is in the shape of the hyperbola y2−x2=33y ^ { 2 } - x ^ { 2 } = 33y2−x2=33 , where xxx and yyy are in meters. Refer to the figure and determine the height hhh of the outside walls. a=b=7ma = b = 7 ma=b=7m

Graph the curve whose parametric equations are given. - x=2t2x=2 t^{2}x=2t2 , y=t+2y=t+2y=t+2 : −∞<t<∞- \infty < t < \infty−∞<t<∞ A) B) C) D)

Find the center, foci, and vertices of the ellipse. - 4x2+64y2=2564 x ^ { 2 } + 64 y ^ { 2 } = 2564x2+64y2=256

Find an equation for the ellipse described. -Center at (0,0)( 0,0 )(0,0) ; focus at (−5,0);( - 5,0 ) ;(−5,0); vertex at (8,0)( 8,0 )(8,0)

Match the equation to its graph. - x2=−12yx ^ { 2 } = - 12 yx2=−12y

Discuss the equation and graph it. - r=63−3cos⁡θr=\frac{6}{3-3 \cos \theta}r=3−3cosθ6​

Graph the hyperbola. - x24−y236=1\frac{x^{2}}{4}-\frac{y^{2}}{36}=14x2​−36y2​=1

Identify the conic that the polar equation represents. Also, give the position of the directrix. - r=21−2cos⁡θr = \frac { 2 } { 1 - 2 \cos \theta }r=1−2cosθ2​

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 center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$

Match the equation to the graph. - $Match the equation to the graph. - A) x ^ { 2 } = 4 y B) x ^ { 2 } = - 4 y C) y ^ { 2 } = 4 x D) y ^ { 2 } = - 4 x$ A) $x ^ { 2 } = 4 y$ B) $x ^ { 2 } = - 4 y$ C) $y ^ { 2 } = 4 x$ D) $y ^ { 2 } = - 4 x$

Find an equation for the hyperbola described. -Vertices at $( \pm 2,0 )$ ; foci at $( \pm 11,0 )$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati - $x^{2}+2 x y+y^{2}-8 x+8 y=0$

Match the equation to its graph. - $y ^ { 2 } = - 10 x$

Match the equation to its graph. - $x ^ { 2 } = 7 y$

Graph the hyperbola. - $(x-2)^{2}-4(y-2)^{2}=4$ $Graph the hyperbola. - (x-2)^{2}-4(y-2)^{2}=4$

Graph the hyperbola. - $\frac{(x-2)^{2}}{4}-\frac{(y-2)^{2}}{16}=1$ $Graph the hyperbola. - \frac{(x-2)^{2}}{4}-\frac{(y-2)^{2}}{16}=1$

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 6 } { 3 - 4 \cos \theta }$

Find the center, foci, and vertices of the ellipse. - $4 x ^ { 2 } + 64 y ^ { 2 } = 256$

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( - 5,0 ) ;$ vertex at $( 8,0 )$

Match the equation to its graph. - $x ^ { 2 } = - 12 y$

Discuss the equation and graph it. - $r=\frac{6}{3-3 \cos \theta}$ $Discuss the equation and graph it. - r=\frac{6}{3-3 \cos \theta}$

Graph the hyperbola. - $\frac{x^{2}}{4}-\frac{y^{2}}{36}=1$ $Graph the hyperbola. - \frac{x^{2}}{4}-\frac{y^{2}}{36}=1$

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 2 } { 1 - 2 \cos \theta }$