Question 1

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
$$4 x ^ { 2 } - 3 y ^ { 2 } - 5 x + 7 y + 1 = 0$$

Accepted Answer

A)  ellipse 
B)  parabola 
C)  hyperbola 
D)  circle 
A)  ellipse 
B)  parabola 
C)  hyperbola 
D)  circle

Question 2

Find the standard form of the equation of the ellipse with the given characteristics.
center: $( - 8 , - 5 ) \quad a = 5 c \quad$ foci: $( - 11 , - 5 ) , ( - 5 , - 5 )$

Accepted Answer

A)  $\frac { ( x - 8 ) ^ { 2 } } { 216 } + \frac { ( y - 5 ) ^ { 2 } } { 225 } = 1$ 
B)  $\frac { ( x + 8 ) ^ { 2 } } { 216 } + \frac { ( y + 5 ) ^ { 2 } } { 225 } = 1$ 
C)  $\frac { ( x + 8 ) ^ { 2 } } { 225 } + \frac { ( y + 5 ) ^ { 2 } } { 216 } = 1$ 
D)  $\frac { ( x + 5 ) ^ { 2 } } { 225 } + \frac { ( y + 8 ) ^ { 2 } } { 216 } = 1$ 
E)  $\frac { ( x - 5 ) ^ { 2 } } { 225 } + \frac { ( y - 8 ) ^ { 2 } } { 216 } = 1$ 
A)  $\frac { ( x - 8 ) ^ { 2 } } { 216 } + \frac { ( y - 5 ) ^ { 2 } } { 225 } = 1$ 
B)  $\frac { ( x + 8 ) ^ { 2 } } { 216 } + \frac { ( y + 5 ) ^ { 2 } } { 225 } = 1$ 
C)  $\frac { ( x + 8 ) ^ { 2 } } { 225 } + \frac { ( y + 5 ) ^ { 2 } } { 216 } = 1$ 
D)  $\frac { ( x + 5 ) ^ { 2 } } { 225 } + \frac { ( y + 8 ) ^ { 2 } } { 216 } = 1$ 
E)  $\frac { ( x - 5 ) ^ { 2 } } { 225 } + \frac { ( y - 8 ) ^ { 2 } } { 216 } = 1$

Question 3

Find the standard form of the parabola with the given characteristics.
focus: $( - 9,7 )$             vertex: $( - 9,6 )$

Accepted Answer

A)  $( x + 9 ) ^ { 2 } = 4 ( y - 6 )$ 
B)  $( x - 9 ) ^ { 2 } = 4 ( y + 6 )$ 
C)  $( x - 6 ) ^ { 2 } = 4 ( y + 9 )$ 
D)  $( x + 6 ) ^ { 2 } = 4 ( y - 9 )$ 
E)  $( x - 9 ) ^ { 2 } = ( y + 6 )$ 
A)  $( x + 9 ) ^ { 2 } = 4 ( y - 6 )$ 
B)  $( x - 9 ) ^ { 2 } = 4 ( y + 6 )$ 
C)  $( x - 6 ) ^ { 2 } = 4 ( y + 9 )$ 
D)  $( x + 6 ) ^ { 2 } = 4 ( y - 9 )$ 
E)  $( x - 9 ) ^ { 2 } = ( y + 6 )$

Question 4

Find the standard form of the equation of the ellipse with the given characteristics. vertices: $( - 6 , - 8 ) , ( - 6,6 ) \quad$ minor axis of length: 10

Accepted Answer

A)  $\frac { ( x - 6 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 49 } = 1$ 
B)  $\frac { ( x + 6 ) ^ { 2 } } { 25 } + \frac { ( y + 1 ) ^ { 2 } } { 49 } = 1$ 
C)  $\frac { ( x + 6 ) ^ { 2 } } { 49 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 49 } + \frac { ( y + 6 ) ^ { 2 } } { 25 } = 1$ 
E)  $\frac { ( x - 1 ) ^ { 2 } } { 49 } + \frac { ( y - 6 ) ^ { 2 } } { 25 } = 1$ 
A)  $\frac { ( x - 6 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 49 } = 1$ 
B)  $\frac { ( x + 6 ) ^ { 2 } } { 25 } + \frac { ( y + 1 ) ^ { 2 } } { 49 } = 1$ 
C)  $\frac { ( x + 6 ) ^ { 2 } } { 49 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 49 } + \frac { ( y + 6 ) ^ { 2 } } { 25 } = 1$ 
E)  $\frac { ( x - 1 ) ^ { 2 } } { 49 } + \frac { ( y - 6 ) ^ { 2 } } { 25 } = 1$

Question 5

Which answer is a polar form of the given rectangular equation?
$$x ^ { 2 } + y ^ { 2 } = 25$$

Accepted Answer

A)  $r = 5$ 
B)  $r = 25$ 
C)  $r ^ { 2 } + \theta ^ { 2 } = 25$ 
D)  $\theta = 25$ 
E)  $\theta = 5$ 
A)  $r = 5$ 
B)  $r = 25$ 
C)  $r ^ { 2 } + \theta ^ { 2 } = 25$ 
D)  $\theta = 25$ 
E)  $\theta = 5$

Question 6

Find an interval for $\theta$ for which the graph is traced only once.
$$r = 2 \sin \left( \frac { 3 \theta } { 2 } \right)$$

Accepted Answer

A)  $0 \leq \theta < \frac { \pi } { 3 }$ 
B)  $0 \leq \theta < \pi$ 
C)  $0 \leq \theta < 4 \pi$ 
D)  $0 \leq \theta < \frac { 4 \pi } { 3 }$ 
E)  $- 2 \pi \leq \theta < 2 \pi$ 
A)  $0 \leq \theta < \frac { \pi } { 3 }$ 
B)  $0 \leq \theta < \pi$ 
C)  $0 \leq \theta < 4 \pi$ 
D)  $0 \leq \theta < \frac { 4 \pi } { 3 }$ 
E)  $- 2 \pi \leq \theta < 2 \pi$

Question 7

Match the graph with its equation.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 3 } - \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 3 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ 
A)  $\frac { x ^ { 2 } } { 3 } - \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 3 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Question 8

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

Accepted Answer

A)  ellipse 
B)  hyperbola 
C)  parabola 
D)  circle 
A)  ellipse 
B)  hyperbola 
C)  parabola 
D)  circle

Question 9

Find the standard form of the parabola with the given characteristic and vertex at the origin.
directrix: $x = 5$

Accepted Answer

A)  $x ^ { 2 } = - 20 y$ 
B)  $x ^ { 2 } = 20 y$ 
C)  $x ^ { 2 } = 5 y$ 
D)  $y ^ { 2 } = 5 x$ 
E)  $y ^ { 2 } = - 20 x$ 
A)  $x ^ { 2 } = - 20 y$ 
B)  $x ^ { 2 } = 20 y$ 
C)  $x ^ { 2 } = 5 y$ 
D)  $y ^ { 2 } = 5 x$ 
E)  $y ^ { 2 } = - 20 x$

Question 10

Which set of parametric equations represents the following line or conic?
Use $x = h + a \sec \theta$ and $y = k + b \tan \theta$.
Hyperbola: vertices $( - 10 , - 1 ) , ( 2 , - 1 )$
foci $( - 11 , - 1 ) , ( 3 , - 1 )$

Accepted Answer

A) 
$\begin{array} { l } 
x = 4 + \sqrt { 13 } \sec \theta \
y = 1 + 6 \tan \theta
\end{array}$ 
B) 
$\begin{array} { l } 
x = - 4 + \sqrt { 13 } \sec \theta \
y = - 1 + 6 \tan \theta
\end{array}$ 
C) 
$\begin{array} { l } 
x = - 1 + \sqrt { 13 } \sec \theta \
y = - 4 + 6 \tan \theta
\end{array}$ 
D) 
$x = - 4 + 6 \sec \theta$
$y = - 1 + \sqrt { 13 } \tan \theta$ 
E) 
$\begin{array} { l } 
x = - 1 + 6 \sec \theta \
y = - 4 + \sqrt { 13 } \tan \theta
\end{array}$ 
A) 
$\begin{array} { l } 
x = 4 + \sqrt { 13 } \sec \theta \
y = 1 + 6 \tan \theta
\end{array}$ 
B) 
$\begin{array} { l } 
x = - 4 + \sqrt { 13 } \sec \theta \
y = - 1 + 6 \tan \theta
\end{array}$ 
C) 
$\begin{array} { l } 
x = - 1 + \sqrt { 13 } \sec \theta \
y = - 4 + 6 \tan \theta
\end{array}$ 
D) 
$x = - 4 + 6 \sec \theta$
$y = - 1 + \sqrt { 13 } \tan \theta$ 
E) 
$\begin{array} { l } 
x = - 1 + 6 \sec \theta \
y = - 4 + \sqrt { 13 } \tan \theta
\end{array}$

Question 11

Find the standard form of the equation of the hyperbola with the given characteristics.
foci: $( \pm 5,0 ) \quad$ asymptotes: $y = \pm 3 x$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$ 
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { \frac { 5 } { 2 } } - \frac { x ^ { 2 } } { \frac { 45 } { 2 } } = 1$ 
D)  $\frac { x ^ { 2 } } { \frac { 5 } { 2 } } - \frac { y ^ { 2 } } { \frac { 45 } { 2 } } = 1$ 
E)  $\frac { x ^ { 2 } } { \frac { 45 } { 2 } } - \frac { y ^ { 2 } } { \frac { 5 } { 2 } } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$ 
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { \frac { 5 } { 2 } } - \frac { x ^ { 2 } } { \frac { 45 } { 2 } } = 1$ 
D)  $\frac { x ^ { 2 } } { \frac { 5 } { 2 } } - \frac { y ^ { 2 } } { \frac { 45 } { 2 } } = 1$ 
E)  $\frac { x ^ { 2 } } { \frac { 45 } { 2 } } - \frac { y ^ { 2 } } { \frac { 5 } { 2 } } = 1$

Question 12

Solve the following system of quadratic equations algebraically by the method of substitution.
$$\left\{ \begin{array} { l } 
8 x ^ { 2 } - 6 y ^ { 2 } + 80 = 0 \
8 x + 4 y = 0
\end{array} \right.$$

Accepted Answer

A)  $( \sqrt { 5 } , - 2 \sqrt { 5 } ) , ( \sqrt { 7 } , - 2 \sqrt { 7 } )$ 
B)  $( - \sqrt { 7 } , 2 \sqrt { 7 } ) , ( \sqrt { 7 } , - 2 \sqrt { 7 } )$ 
C)  $( - \sqrt { 7 } , - 2 \sqrt { 7 } ) , ( \sqrt { 7 } , - 2 \sqrt { 7 } )$ 
D)  $( - \sqrt { 5 } , - 2 \sqrt { 5 } ) , ( \sqrt { 5 } , 2 \sqrt { 5 } )$ 
E)  $( - \sqrt { 5 } , 2 \sqrt { 5 } ) , ( \sqrt { 5 } , - 2 \sqrt { 5 } )$ 
A)  $( \sqrt { 5 } , - 2 \sqrt { 5 } ) , ( \sqrt { 7 } , - 2 \sqrt { 7 } )$ 
B)  $( - \sqrt { 7 } , 2 \sqrt { 7 } ) , ( \sqrt { 7 } , - 2 \sqrt { 7 } )$ 
C)  $( - \sqrt { 7 } , - 2 \sqrt { 7 } ) , ( \sqrt { 7 } , - 2 \sqrt { 7 } )$ 
D)  $( - \sqrt { 5 } , - 2 \sqrt { 5 } ) , ( \sqrt { 5 } , 2 \sqrt { 5 } )$ 
E)  $( - \sqrt { 5 } , 2 \sqrt { 5 } ) , ( \sqrt { 5 } , - 2 \sqrt { 5 } )$

Question 13

Find the standard form of the equation of the hyperbola with the given characteristics.
foci: $( \pm 3,0 ) \quad$ asymptotes: $y = \pm 4 x$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { \frac { 9 } { 17 } } - \frac { x ^ { 2 } } { \frac { 144 } { 17 } } = 1$ 
D)  $\frac { x ^ { 2 } } { \frac { 9 } { 17 } } - \frac { y ^ { 2 } } { \frac { 144 } { 17 } } = 1$ 
E)  $\frac { x ^ { 2 } } { \frac { 144 } { 17 } } - \frac { y ^ { 2 } } { \frac { 9 } { 17 } } = 1$ 
A)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { \frac { 9 } { 17 } } - \frac { x ^ { 2 } } { \frac { 144 } { 17 } } = 1$ 
D)  $\frac { x ^ { 2 } } { \frac { 9 } { 17 } } - \frac { y ^ { 2 } } { \frac { 144 } { 17 } } = 1$ 
E)  $\frac { x ^ { 2 } } { \frac { 144 } { 17 } } - \frac { y ^ { 2 } } { \frac { 9 } { 17 } } = 1$

Question 14

Find a polar equation of the conic with the given characteristics and with one focus at the pole.
$\begin{array}{cl}
\text { Conic } & \text { Vertices } \
\text { Hyperbola } & \left(\frac{2}{3}, \frac{\pi}{2}\right),\left(-2, \frac{3 \pi}{2}\right)
\end{array}$

Accepted Answer

A)  $r = \frac { 2 } { 1 - 2 \sin \theta }$ 
B)  $r = \frac { 2 } { 1 + 2 \sin \theta }$ 
C)  $r = \frac { 2 } { 1 + 2 \cos \theta }$ 
D)  $r = \frac { 2 } { 1 - 2 \cos \theta }$ 
E)  $r = \frac { 2 } { 1 + 1 \cos \theta }$ 
A)  $r = \frac { 2 } { 1 - 2 \sin \theta }$ 
B)  $r = \frac { 2 } { 1 + 2 \sin \theta }$ 
C)  $r = \frac { 2 } { 1 + 2 \cos \theta }$ 
D)  $r = \frac { 2 } { 1 - 2 \cos \theta }$ 
E)  $r = \frac { 2 } { 1 + 1 \cos \theta }$

Question 15

Test the graph of the following equation for symmetry with respect to $\theta = \frac { \pi } { 2 }$, the polar axis, and the pole.
$$r = 2 - 2 \sin ( 4 \theta )$$

Accepted Answer

A)  The graph is symmetric with respect to $\theta = \frac { \pi } { 2 }$ only. 
B)  The graph is symmetric with respect to the pole only. 
C)  The graph is symmetric with respect to all three. 
D)  The graph has no symmetries. 
E)  The graph is symmetric with respect to the polar axis only. 
A)  The graph is symmetric with respect to $\theta = \frac { \pi } { 2 }$ only. 
B)  The graph is symmetric with respect to the pole only. 
C)  The graph is symmetric with respect to all three. 
D)  The graph has no symmetries. 
E)  The graph is symmetric with respect to the polar axis only.

Question 16

Find a polar equation of the conic with the given characteristics and with one focus at the pole.
$\begin{array} { l c c } \text { Conic } & \text { Eccentricity } & \text { Directrix } \ \text { Ellipse } & e = \frac { 1 } { 2 } & y = 5 \end{array}$

Accepted Answer

A)  $r = \frac { 1 } { 2 + \cos \theta }$ 
B)  $r = \frac { 5 } { 2 + \cos \theta }$ 
C)  $r = \frac { 5 } { 2 - \cos \theta }$ 
D)  $r = \frac { 5 } { 2 - \sin \theta }$ 
E)  $r = \frac { 5 } { 2 + \sin \theta }$ 
A)  $r = \frac { 1 } { 2 + \cos \theta }$ 
B)  $r = \frac { 5 } { 2 + \cos \theta }$ 
C)  $r = \frac { 5 } { 2 - \cos \theta }$ 
D)  $r = \frac { 5 } { 2 - \sin \theta }$ 
E)  $r = \frac { 5 } { 2 + \sin \theta }$

Question 17

Which set of parametric equations represents the following line or conic?
Use $x = h + a \sec \theta$ and $y = k + b \tan \theta$.
$\begin{array} { c l } \text { Hyperbola: vertices } & ( 5 , - 3 ) , ( 11 , - 3 ) \ \text { foci } & ( 0 , - 3 ) , ( 16 , - 3 ) \end{array}$

Accepted Answer

A) 
$\begin{array} { l } 
x = - 8 + \sqrt { 55 } \sec \theta \
y = 3 + 3 \tan \theta
\end{array}$ 
B) 
$\begin{array} { l } 
x = 8 + \sqrt { 55 } \sec \theta \
y = - 3 + 3 \tan \theta
\end{array}$ 
C) 
$\begin{array} { l } 
x = - 3 + \sqrt { 55 } \sec \theta \
y = 8 + 3 \tan \theta
\end{array}$ 
D) 
$x = 8 + 3 \sec \theta$
$y = - 3 + \sqrt { 55 } \tan \theta$ 
E) 
$\begin{array} { l } 
x = - 3 + 3 \sec \theta \
y = 8 + \sqrt { 55 } \tan \theta
\end{array}$ 
A) 
$\begin{array} { l } 
x = - 8 + \sqrt { 55 } \sec \theta \
y = 3 + 3 \tan \theta
\end{array}$ 
B) 
$\begin{array} { l } 
x = 8 + \sqrt { 55 } \sec \theta \
y = - 3 + 3 \tan \theta
\end{array}$ 
C) 
$\begin{array} { l } 
x = - 3 + \sqrt { 55 } \sec \theta \
y = 8 + 3 \tan \theta
\end{array}$ 
D) 
$x = 8 + 3 \sec \theta$
$y = - 3 + \sqrt { 55 } \tan \theta$ 
E) 
$\begin{array} { l } 
x = - 3 + 3 \sec \theta \
y = 8 + \sqrt { 55 } \tan \theta
\end{array}$

Question 18

Find a polar equation of the conic with the given characteristics and with one focus at the pole.
$\begin{array} { c c c } \text { Conic } & \text { Eccentricity } & \text { Directrix } \ \text { Hyperbola } & e = 5 & x = 2 \end{array}$

Accepted Answer

A)  $r = \frac { 10 } { 1 - 5 \cos \theta }$ 
B)  $r = \frac { 10 } { 1 + 5 \cos \theta }$ 
C)  $r = \frac { 2 } { 1 + 5 \cos \theta }$ 
D)  $r = \frac { 10 } { 1 + 5 \sin \theta }$ 
E)  $r = \frac { 10 } { 1 - 5 \sin \theta }$ 
A)  $r = \frac { 10 } { 1 - 5 \cos \theta }$ 
B)  $r = \frac { 10 } { 1 + 5 \cos \theta }$ 
C)  $r = \frac { 2 } { 1 + 5 \cos \theta }$ 
D)  $r = \frac { 10 } { 1 + 5 \sin \theta }$ 
E)  $r = \frac { 10 } { 1 - 5 \sin \theta }$

Question 19

Use a graphing utility to graph the rotated conic.
$r = \frac { 1 } { 1 + 2 \cos ( \theta + \pi / 4 ) }$
Use either grid below for your graph, whichever is more convenie

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 20

Rotate the axes to eliminate the $x y$-term in the following equation and then write the equation in standard form.
$$7 x ^ { 2 } - 28 x y + 28 y ^ { 2 } + 35 \sqrt { 5 } y + 7 = 0$$

Accepted Answer

A)  $\left( x ^ { \prime } - 1 \right) ^ { 2 } = 7 \left( y ^ { \prime } - \frac { 4 } { 5 } \right)$ 
B)  $\left( x ^ { \prime } + 7 \right) ^ { 2 } = - 5 \left( y ^ { \prime } + \frac { 1 } { 7 } \right)$ 
C)  $\left( y ^ { \prime } + 1 \right) ^ { 2 } = - \left( x ^ { \prime } - \frac { 4 } { 5 } \right)$ 
D)  $\left( y ^ { \prime } - \frac { 4 } { 5 } \right) ^ { 2 } = 7 \left( x ^ { \prime } - 1 \right)$ 
E)  $\left( y ^ { \prime } + \frac { 4 } { 5 } \right) ^ { 2 } = x ^ { \prime } + \frac { 1 } { 7 }$ 
A)  $\left( x ^ { \prime } - 1 \right) ^ { 2 } = 7 \left( y ^ { \prime } - \frac { 4 } { 5 } \right)$ 
B)  $\left( x ^ { \prime } + 7 \right) ^ { 2 } = - 5 \left( y ^ { \prime } + \frac { 1 } { 7 } \right)$ 
C)  $\left( y ^ { \prime } + 1 \right) ^ { 2 } = - \left( x ^ { \prime } - \frac { 4 } { 5 } \right)$ 
D)  $\left( y ^ { \prime } - \frac { 4 } { 5 } \right) ^ { 2 } = 7 \left( x ^ { \prime } - 1 \right)$ 
E)  $\left( y ^ { \prime } + \frac { 4 } { 5 } \right) ^ { 2 } = x ^ { \prime } + \frac { 1 } { 7 }$

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $4 x ^ { 2 } - 3 y ^ { 2 } - 5 x + 7 y + 1 = 0$

Find the standard form of the equation of the ellipse with the given characteristics. center: $( - 8 , - 5 ) \quad a = 5 c \quad$ foci: $( - 11 , - 5 ) , ( - 5 , - 5 )$

Find the standard form of the parabola with the given characteristics. focus: $( - 9,7 )$ vertex: $( - 9,6 )$

Find the standard form of the equation of the ellipse with the given characteristics. vertices: $( - 6 , - 8 ) , ( - 6,6 ) \quad$ minor axis of length: 10

Which answer is a polar form of the given rectangular equation? $x ^ { 2 } + y ^ { 2 } = 25$

Find an interval for $\theta$ for which the graph is traced only once. $r = 2 \sin \left( \frac { 3 \theta } { 2 } \right)$

Match the graph with its equation.

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

Find the standard form of the parabola with the given characteristic and vertex at the origin. directrix: $x = 5$

Which set of parametric equations represents the following line or conic? Use $x = h + a \sec \theta$ and $y = k + b \tan \theta$ . Hyperbola: vertices $( - 10 , - 1 ) , ( 2 , - 1 )$ foci $( - 11 , - 1 ) , ( 3 , - 1 )$

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 5,0 ) \quad$ asymptotes: $y = \pm 3 x$

Solve the following system of quadratic equations algebraically by the method of substitution. $\left\{ \begin{array} { l } 8 x ^ { 2 } - 6 y ^ { 2 } + 80 = 0 \\8 x + 4 y = 0\end{array} \right.$

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 3,0 ) \quad$ asymptotes: $y = \pm 4 x$

Find a polar equation of the conic with the given characteristics and with one focus at the pole. Conic Vertices Hyperbola , , -2,

Test the graph of the following equation for symmetry with respect to $\theta = \frac { \pi } { 2 }$ , the polar axis, and the pole. $r = 2 - 2 \sin ( 4 \theta )$

Find a polar equation of the conic with the given characteristics and with one focus at the pole. Conic Eccentricity Directrix Ellipse e= y=5

Which set of parametric equations represents the following line or conic? Use $x = h + a \sec \theta$ and $y = k + b \tan \theta$ . Hyperbola: vertices (5,-3),(11,-3) foci (0,-3),(16,-3)

Find a polar equation of the conic with the given characteristics and with one focus at the pole. Conic Eccentricity Directrix Hyperbola e=5 x=2

Rotate the axes to eliminate the $x y$ -term in the following equation and then write the equation in standard form. $7 x ^ { 2 } - 28 x y + 28 y ^ { 2 } + 35 \sqrt { 5 } y + 7 = 0$

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Exam 9: Topics in Analytic Geometry

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 4x2−3y2−5x+7y+1=04 x ^ { 2 } - 3 y ^ { 2 } - 5 x + 7 y + 1 = 04x2−3y2−5x+7y+1=0

Find the standard form of the equation of the ellipse with the given characteristics. center: (−8,−5)a=5c( - 8 , - 5 ) \quad a = 5 c \quad(−8,−5)a=5c foci: (−11,−5),(−5,−5)( - 11 , - 5 ) , ( - 5 , - 5 )(−11,−5),(−5,−5)

Find the standard form of the parabola with the given characteristics. focus: (−9,7)( - 9,7 )(−9,7) vertex: (−9,6)( - 9,6 )(−9,6)

Find the standard form of the equation of the ellipse with the given characteristics. vertices: (−6,−8),(−6,6)( - 6 , - 8 ) , ( - 6,6 ) \quad(−6,−8),(−6,6) minor axis of length: 10

Which answer is a polar form of the given rectangular equation? x2+y2=25x ^ { 2 } + y ^ { 2 } = 25x2+y2=25

Find an interval for θ\thetaθ for which the graph is traced only once. r=2sin⁡(3θ2)r = 2 \sin \left( \frac { 3 \theta } { 2 } \right)r=2sin(23θ​)

Match the graph with its equation.

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola. 2x2+5y2+8x−2y=02 x ^ { 2 } + 5 y ^ { 2 } + 8 x - 2 y = 02x2+5y2+8x−2y=0

Find the standard form of the parabola with the given characteristic and vertex at the origin. directrix: x=5x = 5x=5

Find the standard form of the equation of the hyperbola with the given characteristics. foci: (±5,0)( \pm 5,0 ) \quad(±5,0) asymptotes: y=±3xy = \pm 3 xy=±3x

Solve the following system of quadratic equations algebraically by the method of substitution. {8x2−6y2+80=08x+4y=0\left\{ \begin{array} { l } 8 x ^ { 2 } - 6 y ^ { 2 } + 80 = 0 \\8 x + 4 y = 0\end{array} \right.{8x2−6y2+80=08x+4y=0​

Find the standard form of the equation of the hyperbola with the given characteristics. foci: (±3,0)( \pm 3,0 ) \quad(±3,0) asymptotes: y=±4xy = \pm 4 xy=±4x

Find a polar equation of the conic with the given characteristics and with one focus at the pole. Conic Vertices Hyperbola , , -2,

Test the graph of the following equation for symmetry with respect to θ=π2\theta = \frac { \pi } { 2 }θ=2π​ , the polar axis, and the pole. r=2−2sin⁡(4θ)r = 2 - 2 \sin ( 4 \theta )r=2−2sin(4θ)

Find a polar equation of the conic with the given characteristics and with one focus at the pole. Conic Eccentricity Directrix Ellipse e= y=5

Which set of parametric equations represents the following line or conic? Use x=h+asec⁡θx = h + a \sec \thetax=h+asecθ and y=k+btan⁡θy = k + b \tan \thetay=k+btanθ . Hyperbola: vertices (5,-3),(11,-3) foci (0,-3),(16,-3)

Find a polar equation of the conic with the given characteristics and with one focus at the pole. Conic Eccentricity Directrix Hyperbola e=5 x=2

Use a graphing utility to graph the rotated conic. r=11+2cos⁡(θ+π/4)r = \frac { 1 } { 1 + 2 \cos ( \theta + \pi / 4 ) }r=1+2cos(θ+π/4)1​ Use either grid below for your graph, whichever is more convenie

Rotate the axes to eliminate the xyx yxy -term in the following equation and then write the equation in standard form. 7x2−28xy+28y2+355y+7=07 x ^ { 2 } - 28 x y + 28 y ^ { 2 } + 35 \sqrt { 5 } y + 7 = 07x2−28xy+28y2+355​y+7=0

Functions and Their Graphs

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Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $4 x ^ { 2 } - 3 y ^ { 2 } - 5 x + 7 y + 1 = 0$

Find the standard form of the equation of the ellipse with the given characteristics. center: $( - 8 , - 5 ) \quad a = 5 c \quad$ foci: $( - 11 , - 5 ) , ( - 5 , - 5 )$

Find the standard form of the parabola with the given characteristics. focus: $( - 9,7 )$ vertex: $( - 9,6 )$

Find the standard form of the equation of the ellipse with the given characteristics. vertices: $( - 6 , - 8 ) , ( - 6,6 ) \quad$ minor axis of length: 10

Which answer is a polar form of the given rectangular equation? $x ^ { 2 } + y ^ { 2 } = 25$

Find an interval for $\theta$ for which the graph is traced only once. $r = 2 \sin \left( \frac { 3 \theta } { 2 } \right)$

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

Find the standard form of the parabola with the given characteristic and vertex at the origin. directrix: $x = 5$

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 5,0 ) \quad$ asymptotes: $y = \pm 3 x$

Solve the following system of quadratic equations algebraically by the method of substitution. $\left\{ \begin{array} { l } 8 x ^ { 2 } - 6 y ^ { 2 } + 80 = 0 \\8 x + 4 y = 0\end{array} \right.$

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 3,0 ) \quad$ asymptotes: $y = \pm 4 x$

Test the graph of the following equation for symmetry with respect to $\theta = \frac { \pi } { 2 }$ , the polar axis, and the pole. $r = 2 - 2 \sin ( 4 \theta )$

Which set of parametric equations represents the following line or conic? Use $x = h + a \sec \theta$ and $y = k + b \tan \theta$ . Hyperbola: vertices (5,-3),(11,-3) foci (0,-3),(16,-3)

Rotate the axes to eliminate the $x y$ -term in the following equation and then write the equation in standard form. $7 x ^ { 2 } - 28 x y + 28 y ^ { 2 } + 35 \sqrt { 5 } y + 7 = 0$