Question 1

Find the standard form of the parabola with the given characteristic and vertex at the origin.
focus: $( 0 , - 5 )$

Accepted Answer

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

Question 2

Use the Quadratic Formula to solve for $y$ in the following equation.
$$36 x ^ { 2 } - 84 x y + 49 y ^ { 2 } - 70 x - 30 y = 0$$

Accepted Answer

A)  $\frac { - 42 x - 15 \pm \sqrt { - 84 x + 3655 } } { 49 }$ 
B)  $\frac { 2 ( 42 x + 15 ) \pm \sqrt { - 84 x + 14620 } } { 49 }$ 
C)  $\frac { 42 x + 15 \pm \sqrt { 4690 x + 225 } } { 49 }$ 
D)  $\frac { 84 x + 30 \pm \sqrt { - 42 x + 7085 } } { 98 }$ 
E)  $\frac { - 84 x - 30 \pm \sqrt { - 42 x + 4330 } } { 98 }$ 
A)  $\frac { - 42 x - 15 \pm \sqrt { - 84 x + 3655 } } { 49 }$ 
B)  $\frac { 2 ( 42 x + 15 ) \pm \sqrt { - 84 x + 14620 } } { 49 }$ 
C)  $\frac { 42 x + 15 \pm \sqrt { 4690 x + 225 } } { 49 }$ 
D)  $\frac { 84 x + 30 \pm \sqrt { - 42 x + 7085 } } { 98 }$ 
E)  $\frac { - 84 x - 30 \pm \sqrt { - 42 x + 4330 } } { 98 }$

Question 3

Find the eccentricity of the following ellipse. Round your answer to two decimals.
$$2 x ^ { 2 } + 5 y ^ { 2 } - 4 x + 10 y - 10 = 0$$

Accepted Answer

A)  $1.50$ 
B)  $1.07$ 
C)  $60.69$ 
D)  $0.77$ 
E)  $ 0.63$ 
A)  $1.50$ 
B)  $1.07$ 
C)  $60.69$ 
D)  $0.77$ 
E)  $ 0.63$

Question 4

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola.
$$3 y ^ { 2 } + 17 x + y - 103 = 0$$

Accepted Answer

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

Question 5

Find the standard form of the equation of the ellipse below.
$$8 x ^ { 2 } + 4 y ^ { 2 } + 64 x - 32 y + 32 = 0$$

Accepted Answer

A)  $\frac { ( x - 4 ) ^ { 2 } } { ( 2 \sqrt { 5 } ) ^ { 2 } } + \frac { ( y + 4 ) ^ { 2 } } { ( 2 \sqrt { 10 } ) ^ { 2 } } = 1$ 
B)  $\frac { ( x + 4 ) ^ { 2 } } { ( 2 \sqrt { 5 } ) ^ { 2 } } + \frac { ( y - 4 ) ^ { 2 } } { ( 2 \sqrt { 10 } ) ^ { 2 } } = 1$ 
C)  $\frac { ( x + 4 ) ^ { 2 } } { ( 2 \sqrt { 10 } ) ^ { 2 } } - \frac { ( y - 4 ) ^ { 2 } } { ( 2 \sqrt { 5 } ) ^ { 2 } } = 1$ 
D)  $\frac { ( x - 4 ) ^ { 2 } } { ( 2 \sqrt { 10 } ) ^ { 2 } } + \frac { ( y + 4 ) ^ { 2 } } { ( 2 \sqrt { 5 } ) ^ { 2 } } = 1$ 
E)  $\frac { ( x - 4 ) ^ { 2 } } { ( 2 \sqrt { 5 } ) ^ { 2 } } - \frac { ( y + 4 ) ^ { 2 } } { ( 2 \sqrt { 10 } ) ^ { 2 } } = 1$ 
A)  $\frac { ( x - 4 ) ^ { 2 } } { ( 2 \sqrt { 5 } ) ^ { 2 } } + \frac { ( y + 4 ) ^ { 2 } } { ( 2 \sqrt { 10 } ) ^ { 2 } } = 1$ 
B)  $\frac { ( x + 4 ) ^ { 2 } } { ( 2 \sqrt { 5 } ) ^ { 2 } } + \frac { ( y - 4 ) ^ { 2 } } { ( 2 \sqrt { 10 } ) ^ { 2 } } = 1$ 
C)  $\frac { ( x + 4 ) ^ { 2 } } { ( 2 \sqrt { 10 } ) ^ { 2 } } - \frac { ( y - 4 ) ^ { 2 } } { ( 2 \sqrt { 5 } ) ^ { 2 } } = 1$ 
D)  $\frac { ( x - 4 ) ^ { 2 } } { ( 2 \sqrt { 10 } ) ^ { 2 } } + \frac { ( y + 4 ) ^ { 2 } } { ( 2 \sqrt { 5 } ) ^ { 2 } } = 1$ 
E)  $\frac { ( x - 4 ) ^ { 2 } } { ( 2 \sqrt { 5 } ) ^ { 2 } } - \frac { ( y + 4 ) ^ { 2 } } { ( 2 \sqrt { 10 } ) ^ { 2 } } = 1$

Question 6

Find the center and foci of the ellipse.
$$\frac { ( x - 9 ) ^ { 2 } } { 32 } + \frac { ( y + 5 ) ^ { 2 } } { 36 } = 1$$

Accepted Answer

A)  center: $( - 9,5 ) \quad$ foci: $( - 9,3 ) , ( - 9,7 )$ 
B)  center: $( 9 , - 5 ) \quad$ foci: $( 9 , - 7 ) , ( 9 , - 3 )$ 
C)  center: $( 9 , - 5 ) \quad$ foci: $( 7 , - 5 ) , ( 11 , - 5 )$ 
D)  center: $( - 9,5 ) \quad$ foci: $( - 11 , - 5 ) , ( - 7 , - 5 )$ 
E)  center: $( 9 , - 5 ) \quad$ foci: $( - 11,5 ) , ( - 7,5 )$ 
A)  center: $( - 9,5 ) \quad$ foci: $( - 9,3 ) , ( - 9,7 )$ 
B)  center: $( 9 , - 5 ) \quad$ foci: $( 9 , - 7 ) , ( 9 , - 3 )$ 
C)  center: $( 9 , - 5 ) \quad$ foci: $( 7 , - 5 ) , ( 11 , - 5 )$ 
D)  center: $( - 9,5 ) \quad$ foci: $( - 11 , - 5 ) , ( - 7 , - 5 )$ 
E)  center: $( 9 , - 5 ) \quad$ foci: $( - 11,5 ) , ( - 7,5 )$

Question 7

Find the center and foci of the following ellipse.
$$4 x ^ { 2 } + 8 y ^ { 2 } - 16 x + 32 y + 32 = 0$$

Accepted Answer

A)  Center: $( - 2,2 )$
Foci: $( - 2 + \sqrt { 2 } , 2 ) , ( - 2 - \sqrt { 2 } , 2 )$ 
B)  Center: $( 2 , - 2 )$
Foci: $( 2 + \sqrt { 2 } , - 2 ) , ( 2 - \sqrt { 2 } , - 2 )$ 
C)  Center: $( 2 , - 2 )$
Foci: $( 2 , - 2 + \sqrt { 2 } ) , ( 2 , - 2 - \sqrt { 2 } )$ 
D)  Center: $( - 2,2 )$
Foci: $( - 2,2 + \sqrt { 2 } ) , ( - 2,2 - \sqrt { 2 } )$ 
E)  Center: $( - 2,2 )$
Foci: $( - 2 + \sqrt { 6 } , 2 ) , ( - 2 - \sqrt { 6 } , - 2 )$ 
A)  Center: $( - 2,2 )$
Foci: $( - 2 + \sqrt { 2 } , 2 ) , ( - 2 - \sqrt { 2 } , 2 )$ 
B)  Center: $( 2 , - 2 )$
Foci: $( 2 + \sqrt { 2 } , - 2 ) , ( 2 - \sqrt { 2 } , - 2 )$ 
C)  Center: $( 2 , - 2 )$
Foci: $( 2 , - 2 + \sqrt { 2 } ) , ( 2 , - 2 - \sqrt { 2 } )$ 
D)  Center: $( - 2,2 )$
Foci: $( - 2,2 + \sqrt { 2 } ) , ( - 2,2 - \sqrt { 2 } )$ 
E)  Center: $( - 2,2 )$
Foci: $( - 2 + \sqrt { 6 } , 2 ) , ( - 2 - \sqrt { 6 } , - 2 )$

Question 8

Use the Quadratic Formula to solve for $y$ in the following equation.
$$49 x ^ { 2 } - 42 x y + 9 y ^ { 2 } - 90 x - 10 y = 0$$

Accepted Answer

A)  $\frac { - 21 x - 5 \pm \sqrt { - 42 x + 835 } } { 9 }$ 
B)  $\frac { 2 ( 21 x + 5 ) \pm \sqrt { - 42 x + 3340 } } { 9 }$ 
C)  $\frac { 21 x + 5 \pm \sqrt { 1020 x + 25 } } { 9 }$ 
D)  $\frac { 42 x + 10 \pm \sqrt { - 21 x + 1645 } } { 18 }$ 
E)  $\frac { - 42 x - 10 \pm \sqrt { - 21 x + 910 } } { 18 }$ 
A)  $\frac { - 21 x - 5 \pm \sqrt { - 42 x + 835 } } { 9 }$ 
B)  $\frac { 2 ( 21 x + 5 ) \pm \sqrt { - 42 x + 3340 } } { 9 }$ 
C)  $\frac { 21 x + 5 \pm \sqrt { 1020 x + 25 } } { 9 }$ 
D)  $\frac { 42 x + 10 \pm \sqrt { - 21 x + 1645 } } { 18 }$ 
E)  $\frac { - 42 x - 10 \pm \sqrt { - 21 x + 910 } } { 18 }$

Question 9

Sketch the graph of the polar equation using symmetry, zeros, maximum $r$-values, and any other additional points. $r = 2 - 3 \cos \theta$
Use either grid below for your graph, whichever is more convenient.

Accepted Answer

symmetry: with respe

Question 10

Use the discriminant to classify the graph; then use the quadratic formula to solve for $y$.
$$3 x ^ { 2 } - 2 \sqrt { 3 } x y + y ^ { 2 } + 10 \sqrt { 3 } x - 6 y - 24 = 0$$

Accepted Answer

A)  ellipse; $y = 3 + \sqrt { 3 } x \pm \sqrt { 4 \sqrt { 3 } x + 33 }$ 
B)  ellipse; $y = 3 + \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }$ 
C)  parabola; $y = 3 + \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }$ 
D)  parabola; $y = \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }$ 
E)  hyperbola; $y = \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }$ 
A)  ellipse; $y = 3 + \sqrt { 3 } x \pm \sqrt { 4 \sqrt { 3 } x + 33 }$ 
B)  ellipse; $y = 3 + \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }$ 
C)  parabola; $y = 3 + \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }$ 
D)  parabola; $y = \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }$ 
E)  hyperbola; $y = \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }$

Question 11

Convert the point from polar coordinates to rectangular coordinates. Round answer to three decimal places, if necessary.
$$\left( 3 , - \frac { 3 \pi } { 2 } \right)$$

Accepted Answer

A)  $( 3,0 )$ 
B)  $( 0,3 )$ 
C)  $( 0 , - 3 )$ 
D)  $( - 3,0 )$ 
E)  $( 3 , - 4.712 )$ 
A)  $( 3,0 )$ 
B)  $( 0,3 )$ 
C)  $( 0 , - 3 )$ 
D)  $( - 3,0 )$ 
E)  $( 3 , - 4.712 )$

Question 12

Find the standard form of the parabola with the given characteristics.
focus: $( 8,13 )$               directrix: $y = - 1$

Accepted Answer

A)  $( x - 8 ) ^ { 2 } = 28 ( y - 6 )$ 
B)  $( x + 8 ) ^ { 2 } = 28 ( y + 6 )$ 
C)  $( x - 6 ) ^ { 2 } = 28 ( y - 8 )$ 
D)  $( x + 6 ) ^ { 2 } = 28 ( y + 8 )$ 
E)  $( x + 8 ) ^ { 2 } = 7 ( y + 6 )$ 
A)  $( x - 8 ) ^ { 2 } = 28 ( y - 6 )$ 
B)  $( x + 8 ) ^ { 2 } = 28 ( y + 6 )$ 
C)  $( x - 6 ) ^ { 2 } = 28 ( y - 8 )$ 
D)  $( x + 6 ) ^ { 2 } = 28 ( y + 8 )$ 
E)  $( x + 8 ) ^ { 2 } = 7 ( y + 6 )$

Question 13

Find the standard form of the equation of the ellipse with the following characteristics.
foci: $( \pm 4,0 )$
major axis of length: 14

Accepted Answer

A)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$ 
B)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$ 
D)  $\frac { x ^ { 2 } } { 196 } + \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 196 } + \frac { y ^ { 2 } } { 180 } = 1$ 
A)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$ 
B)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$ 
D)  $\frac { x ^ { 2 } } { 196 } + \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 196 } + \frac { y ^ { 2 } } { 180 } = 1$

Question 14

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
$$7 x ^ { 2 } + 7 y ^ { 2 } - 7 x + 9 y - 2 = 0$$

Accepted Answer

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

Question 15

Rotate the axes to eliminate the $x y$-term in the equation. Then write the equation in standard form.
$$113 x ^ { 2 } - 30 x y + 113 y ^ { 2 } - 6272 = 0$$

Accepted Answer

A)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 81 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 64 } = 1$ 
B)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 49 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1$ 
C)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 64 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 64 } = 1$ 
D)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 49 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 49 } = 1$ 
E)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 64 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 49 } = 1$ 
A)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 81 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 64 } = 1$ 
B)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 49 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1$ 
C)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 64 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 64 } = 1$ 
D)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 49 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 49 } = 1$ 
E)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 64 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 49 } = 1$

Question 16

Find the standard form of the equation of the following hyperbola.
$10 x ^ { 2 } - 6 y ^ { 2 } = 60$

Accepted Answer

A)  $\frac { x ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } - \frac { y ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 10 ^ { 2 } } - \frac { y ^ { 2 } } { 6 ^ { 2 } } = 1$ 
C)  $\frac { y ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } - \frac { x ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } = 1$ 
D)  $\frac { y ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } - \frac { x ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } = 1$ 
E)  $\frac { x ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } - \frac { y ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } = 1$ 
A)  $\frac { x ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } - \frac { y ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 10 ^ { 2 } } - \frac { y ^ { 2 } } { 6 ^ { 2 } } = 1$ 
C)  $\frac { y ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } - \frac { x ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } = 1$ 
D)  $\frac { y ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } - \frac { x ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } = 1$ 
E)  $\frac { x ^ { 2 } } { ( \sqrt { 10 } ) ^ { 2 } } - \frac { y ^ { 2 } } { ( \sqrt { 6 } ) ^ { 2 } } = 1$

Question 17

Sketch the graph of the polar equation using symmetry, zeros, maximum $r$-values, and any other additional points. $r ^ { 2 } = 4 \sin 2 \theta$
Use either grid below for your graph, whichever is more convenient.

Accepted Answer

symmetry: with respe

Question 18

Find the vertex and focus of the parabola.
$$x ^ { 2 } - 8 y = 0$$

Accepted Answer

A)  vertex: $( 2,0 )$ focus: $( 0,0 )$ 
B)  vertex: $( - 2,0 )$ focus: $( 0,0 )$ 
C)  vertex: $( 0,0 )$ focus: $( 2,0 )$ 
D)  vertex: $( 0,0 )$ focus: $( 0,2 )$ 
E)  vertex: $( 0,0 )$ focus: $( 0 , - 2 )$ 
A)  vertex: $( 2,0 )$ focus: $( 0,0 )$ 
B)  vertex: $( - 2,0 )$ focus: $( 0,0 )$ 
C)  vertex: $( 0,0 )$ focus: $( 2,0 )$ 
D)  vertex: $( 0,0 )$ focus: $( 0,2 )$ 
E)  vertex: $( 0,0 )$ focus: $( 0 , - 2 )$

Question 19

Use a graphing utility to graph the polar equation and show that the indicated line is an asymptote.
$\begin{array} { l c c } \text { Name of Graph } & \text { Polar Equation } & \text { Asymptote } \ \text { Hyperbolic } & r = - \frac { 5 } { \theta } & y = - 5 \ \text { Spiral } & & \end{array}$
Use either grid below for your graph, whichever is more convenient.

Accepted Answer

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

Question 20

Identify the center and radius of the circle below.
$$( x + 1 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 9$$

Accepted Answer

A)  Center: $( - 1,8 )$
Radius: 3 
B)  Center: $( - 1,8 )$
Radius: 9 
C)  Center: $( 1 , - 8 )$
Radius: 3 
D)  Center: $( 1 , - 8 )$
Radius: 9 
E)  Center: $( 8 , - 1 )$
Radius: 3 
A)  Center: $( - 1,8 )$
Radius: 3 
B)  Center: $( - 1,8 )$
Radius: 9 
C)  Center: $( 1 , - 8 )$
Radius: 3 
D)  Center: $( 1 , - 8 )$
Radius: 9 
E)  Center: $( 8 , - 1 )$
Radius: 3

Find the standard form of the parabola with the given characteristic and vertex at the origin. focus: $( 0 , - 5 )$

Use the Quadratic Formula to solve for $y$ in the following equation. $36 x ^ { 2 } - 84 x y + 49 y ^ { 2 } - 70 x - 30 y = 0$

Find the eccentricity of the following ellipse. Round your answer to two decimals. $2 x ^ { 2 } + 5 y ^ { 2 } - 4 x + 10 y - 10 = 0$

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola. $3 y ^ { 2 } + 17 x + y - 103 = 0$

Find the standard form of the equation of the ellipse below. $8 x ^ { 2 } + 4 y ^ { 2 } + 64 x - 32 y + 32 = 0$

Find the center and foci of the ellipse. $\frac { ( x - 9 ) ^ { 2 } } { 32 } + \frac { ( y + 5 ) ^ { 2 } } { 36 } = 1$

Find the center and foci of the following ellipse. $4 x ^ { 2 } + 8 y ^ { 2 } - 16 x + 32 y + 32 = 0$

Use the Quadratic Formula to solve for $y$ in the following equation. $49 x ^ { 2 } - 42 x y + 9 y ^ { 2 } - 90 x - 10 y = 0$

Use the discriminant to classify the graph; then use the quadratic formula to solve for $y$ . $3 x ^ { 2 } - 2 \sqrt { 3 } x y + y ^ { 2 } + 10 \sqrt { 3 } x - 6 y - 24 = 0$

Convert the point from polar coordinates to rectangular coordinates. Round answer to three decimal places, if necessary. $\left( 3 , - \frac { 3 \pi } { 2 } \right)$

Find the standard form of the parabola with the given characteristics. focus: $( 8,13 )$ directrix: $y = - 1$

Find the standard form of the equation of the ellipse with the following characteristics. foci: $( \pm 4,0 )$ major axis of length: 14

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $7 x ^ { 2 } + 7 y ^ { 2 } - 7 x + 9 y - 2 = 0$

Rotate the axes to eliminate the $x y$ -term in the equation. Then write the equation in standard form. $113 x ^ { 2 } - 30 x y + 113 y ^ { 2 } - 6272 = 0$

Find the standard form of the equation of the following hyperbola. $10 x ^ { 2 } - 6 y ^ { 2 } = 60$

Find the vertex and focus of the parabola. $x ^ { 2 } - 8 y = 0$

Identify the center and radius of the circle below. $( x + 1 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 9$

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Exam 9: Topics in Analytic Geometry

Find the standard form of the parabola with the given characteristic and vertex at the origin. focus: (0,−5)( 0 , - 5 )(0,−5)

Use the Quadratic Formula to solve for yyy in the following equation. 36x2−84xy+49y2−70x−30y=036 x ^ { 2 } - 84 x y + 49 y ^ { 2 } - 70 x - 30 y = 036x2−84xy+49y2−70x−30y=0

Find the eccentricity of the following ellipse. Round your answer to two decimals. 2x2+5y2−4x+10y−10=02 x ^ { 2 } + 5 y ^ { 2 } - 4 x + 10 y - 10 = 02x2+5y2−4x+10y−10=0

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola. 3y2+17x+y−103=03 y ^ { 2 } + 17 x + y - 103 = 03y2+17x+y−103=0

Find the standard form of the equation of the ellipse below. 8x2+4y2+64x−32y+32=08 x ^ { 2 } + 4 y ^ { 2 } + 64 x - 32 y + 32 = 08x2+4y2+64x−32y+32=0

Find the center and foci of the ellipse. (x−9)232+(y+5)236=1\frac { ( x - 9 ) ^ { 2 } } { 32 } + \frac { ( y + 5 ) ^ { 2 } } { 36 } = 132(x−9)2​+36(y+5)2​=1

Find the center and foci of the following ellipse. 4x2+8y2−16x+32y+32=04 x ^ { 2 } + 8 y ^ { 2 } - 16 x + 32 y + 32 = 04x2+8y2−16x+32y+32=0

Use the Quadratic Formula to solve for yyy in the following equation. 49x2−42xy+9y2−90x−10y=049 x ^ { 2 } - 42 x y + 9 y ^ { 2 } - 90 x - 10 y = 049x2−42xy+9y2−90x−10y=0

Sketch the graph of the polar equation using symmetry, zeros, maximum rrr -values, and any other additional points. r=2−3cos⁡θr = 2 - 3 \cos \thetar=2−3cosθ Use either grid below for your graph, whichever is more convenient.

Use the discriminant to classify the graph; then use the quadratic formula to solve for yyy . 3x2−23xy+y2+103x−6y−24=03 x ^ { 2 } - 2 \sqrt { 3 } x y + y ^ { 2 } + 10 \sqrt { 3 } x - 6 y - 24 = 03x2−23​xy+y2+103​x−6y−24=0

Convert the point from polar coordinates to rectangular coordinates. Round answer to three decimal places, if necessary. (3,−3π2)\left( 3 , - \frac { 3 \pi } { 2 } \right)(3,−23π​)

Find the standard form of the parabola with the given characteristics. focus: (8,13)( 8,13 )(8,13) directrix: y=−1y = - 1y=−1

Find the standard form of the equation of the ellipse with the following characteristics. foci: (±4,0)( \pm 4,0 )(±4,0) major axis of length: 14

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 7x2+7y2−7x+9y−2=07 x ^ { 2 } + 7 y ^ { 2 } - 7 x + 9 y - 2 = 07x2+7y2−7x+9y−2=0

Rotate the axes to eliminate the xyx yxy -term in the equation. Then write the equation in standard form. 113x2−30xy+113y2−6272=0113 x ^ { 2 } - 30 x y + 113 y ^ { 2 } - 6272 = 0113x2−30xy+113y2−6272=0

Find the standard form of the equation of the following hyperbola. 10x2−6y2=6010 x ^ { 2 } - 6 y ^ { 2 } = 6010x2−6y2=60

Sketch the graph of the polar equation using symmetry, zeros, maximum rrr -values, and any other additional points. r2=4sin⁡2θr ^ { 2 } = 4 \sin 2 \thetar2=4sin2θ Use either grid below for your graph, whichever is more convenient.

Find the vertex and focus of the parabola. x2−8y=0x ^ { 2 } - 8 y = 0x2−8y=0

Use a graphing utility to graph the polar equation and show that the indicated line is an asymptote. Name of Graph Polar Equation Asymptote Hyperbolic r=- y=-5 Spiral Use either grid below for your graph, whichever is more convenient.

Identify the center and radius of the circle below. (x+1)2+(y−8)2=9( x + 1 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 9(x+1)2+(y−8)2=9