Question 1

Select correct graph to graph rotated conic.  $r = \frac { 6 } { 6 + \sin ( \theta - \pi / 3 ) }$

Accepted Answer

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

Question 2

Find the angle $\theta$ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $\begin{array} { l } 
12 x + 6 y = 18 \
3 x - 2 y = - 1
\end{array}$

Accepted Answer

A)  $\Theta \approx 1.1071 \text { radians } \approx 64.4 ^ { \circ }$ 
B)  $\theta \approx 1.1071 \text { radians } \approx 62.4 ^ { \circ }$ 
C)  $\theta \approx 1.1071 \text { radians } \approx 65.4 ^ { \circ }$ 
D)  $\theta \approx 1.1071 \text { radians } \approx 63.4 ^ { \circ }$ 
E)  $\theta \approx 1.1071 \text { radians } \approx 61.4 ^ { \circ }$ 
A)  $\Theta \approx 1.1071 \text { radians } \approx 64.4 ^ { \circ }$ 
B)  $\theta \approx 1.1071 \text { radians } \approx 62.4 ^ { \circ }$ 
C)  $\theta \approx 1.1071 \text { radians } \approx 65.4 ^ { \circ }$ 
D)  $\theta \approx 1.1071 \text { radians } \approx 63.4 ^ { \circ }$ 
E)  $\theta \approx 1.1071 \text { radians } \approx 61.4 ^ { \circ }$

Question 3

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. 
Vertices: $( \pm 4,0 )$ ; foci: $( \pm 8,0 )$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 48 } - \frac { x ^ { 2 } } { 16 } = 1$ 
B)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 48 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 48 } = 1$ 
D)  $\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 48 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$ 
A)  $\frac { y ^ { 2 } } { 48 } - \frac { x ^ { 2 } } { 16 } = 1$ 
B)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 48 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 48 } = 1$ 
D)  $\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 48 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$

Question 4

Use the Quadratic Formula to solve for $y$ .  $x ^ { 2 } - 12 x y - 10 y ^ { 2 } - 22 = 0$

Accepted Answer

A)  $y = \frac { 12 x \pm \sqrt { 144 x ^ { 2 } + 40 \left( x ^ { 2 } + 22 \right) } } { - 20 }$ 
B)  $y = \frac { 12 x \pm \sqrt { 144 x ^ { 2 } + 40 \left( x ^ { 2 } - 22 \right) } } { - 20 }$ 
C)  $y = \frac { 12 x \pm \sqrt { 144 x ^ { 2 } + 40 \left( x ^ { 2 } - 22 \right) } } { 20 }$ 
D)  $y = \frac { 12 x \pm \sqrt { 144 x + 40 \left( x ^ { 2 } - 22 \right) } } { - 20 }$ 
E)  $y = \frac { 12 x \pm \sqrt { 144 x ^ { 2 } + 40 \left( x ^ { 2 } + 22 \right) } } { 20 }$ 
A)  $y = \frac { 12 x \pm \sqrt { 144 x ^ { 2 } + 40 \left( x ^ { 2 } + 22 \right) } } { - 20 }$ 
B)  $y = \frac { 12 x \pm \sqrt { 144 x ^ { 2 } + 40 \left( x ^ { 2 } - 22 \right) } } { - 20 }$ 
C)  $y = \frac { 12 x \pm \sqrt { 144 x ^ { 2 } + 40 \left( x ^ { 2 } - 22 \right) } } { 20 }$ 
D)  $y = \frac { 12 x \pm \sqrt { 144 x + 40 \left( x ^ { 2 } - 22 \right) } } { - 20 }$ 
E)  $y = \frac { 12 x \pm \sqrt { 144 x ^ { 2 } + 40 \left( x ^ { 2 } + 22 \right) } } { 20 }$

Question 5

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. 
Vertices: (0,±2); asymptotes: y = ± $\frac { 3 } { 2 }$ x

Accepted Answer

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

Question 6

Find the angle $\theta$ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.  $$\begin{array} { l } 
x - y = 0 \
5 x - 4 y = - 3
\end{array}$$

Accepted Answer

A)  $\Theta \approx 0.1107 \text { radian } \approx 7.3 ^ { \circ }$ 
B)  $\Theta \approx 0.1107 \text { radian } \approx 5.3 ^ { \circ }$ 
C)  $\Theta \approx 0.1107 \text { radian } \approx 6.3 ^ { \circ }$ 
D)  $\Theta \approx 0.1107 \text { radian } \approx 8.3 ^ { \circ }$ 
E)  $\Theta \approx 0.1107 \text { radian } \approx 4.3 ^ { \circ }$ 
A)  $\Theta \approx 0.1107 \text { radian } \approx 7.3 ^ { \circ }$ 
B)  $\Theta \approx 0.1107 \text { radian } \approx 5.3 ^ { \circ }$ 
C)  $\Theta \approx 0.1107 \text { radian } \approx 6.3 ^ { \circ }$ 
D)  $\Theta \approx 0.1107 \text { radian } \approx 8.3 ^ { \circ }$ 
E)  $\Theta \approx 0.1107 \text { radian } \approx 4.3 ^ { \circ }$

Question 7

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = 5 \cos 2 \theta$

Accepted Answer

A) Symmetric with respect to the polar axis $\begin{array} { c } 
| r | = 5 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
\end{array}$   
B) Symmetric with respect to the polar axis $\begin{array} { c } 
| r | = 5 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
\end{array}$   
C) Symmetric with respect to the polar axis $\begin{array} { c } 
| r | = 5 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
\end{array}$    
D) Symmetric with respect to the polar axis $\begin{array} { c } 
| r | = 5 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
\end{array}$    
E) Symmetric with respect to the polar axis $\begin{array} { c } 
| r | = 5 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
\end{array}$    
A) Symmetric with respect to the polar axis $\begin{array} { c } 
| r | = 5 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
\end{array}$   
B) Symmetric with respect to the polar axis $\begin{array} { c } 
| r | = 5 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
\end{array}$   
C) Symmetric with respect to the polar axis $\begin{array} { c } 
| r | = 5 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
\end{array}$    
D) Symmetric with respect to the polar axis $\begin{array} { c } 
| r | = 5 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
\end{array}$    
E) Symmetric with respect to the polar axis $\begin{array} { c } 
| r | = 5 \text { when } \theta = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }
\end{array}$

Question 8

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 9

Find the center and vertices of the hyperbola and sketch its graph, using asymptotes as sketching aids.  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$

Accepted Answer

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

Question 10

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.  $\begin{array} { l } 
x = 4 \cos \theta \
y = 2 \sin \theta
\end{array}$

Accepted Answer

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

Question 11

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 1 } { 7 } x$

Accepted Answer

A) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( 0 , - \frac { 1 } { 28 } \right)$ 
B) vertex: $\left( 0 , \frac { 5 } { 4 } \right)$ focus: $\left( - \frac { 1 } { 7 } , - \frac { 1 } { 7 } \right)$ 
C) vertex: (0, 0) focus: $\left( - \frac { 1 } { 28 } , 0 \right)$ 
D) vertex: (0, 0) focus: $\left( - \frac { 1 } { 7 } , 0 \right)$ 
E) vertex: (0, 0) focus: $\left( 0 , - \frac { 1 } { 7 } \right)$ 
A) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( 0 , - \frac { 1 } { 28 } \right)$ 
B) vertex: $\left( 0 , \frac { 5 } { 4 } \right)$ focus: $\left( - \frac { 1 } { 7 } , - \frac { 1 } { 7 } \right)$ 
C) vertex: (0, 0) focus: $\left( - \frac { 1 } { 28 } , 0 \right)$ 
D) vertex: (0, 0) focus: $\left( - \frac { 1 } { 7 } , 0 \right)$ 
E) vertex: (0, 0) focus: $\left( 0 , - \frac { 1 } { 7 } \right)$

Question 12

The $x ^ { \prime } y ^ { \prime }$ -coordinate system has been rotated $\theta$ degrees from the $x y$ -coordinate system.The coordinates of a point in the $x y$ -coordinate system are given.Find the coordinates of the point in the rotated coordinate system.  $\theta = 30 ^ { \circ }$ , $( 2,6 )$

Accepted Answer

A)  $( \sqrt { 3 } + 3,3 \sqrt { 3 } + 1 )$ 
B)  $( \sqrt { 3 } + 3,3 \sqrt { 3 } - 1 )$ 
C)  $\left( \frac { 3 - \sqrt { 3 } } { 2 } , \frac { 3 \sqrt { 3 } + 1 } { 2 } \right)$ 
D)  $( \sqrt { 3 } - 3,3 \sqrt { 3 } - 1 )$ 
E)  $\left( \frac { 3 - \sqrt { 3 } } { 2 } , \frac { 3 \sqrt { 3 } + 3 } { 2 } \right)$ 
A)  $( \sqrt { 3 } + 3,3 \sqrt { 3 } + 1 )$ 
B)  $( \sqrt { 3 } + 3,3 \sqrt { 3 } - 1 )$ 
C)  $\left( \frac { 3 - \sqrt { 3 } } { 2 } , \frac { 3 \sqrt { 3 } + 1 } { 2 } \right)$ 
D)  $( \sqrt { 3 } - 3,3 \sqrt { 3 } - 1 )$ 
E)  $\left( \frac { 3 - \sqrt { 3 } } { 2 } , \frac { 3 \sqrt { 3 } + 3 } { 2 } \right)$

Question 13

Graph the hyperbola.  $9 y ^ { 2 } - 16 x ^ { 2 } + 36 y + 64 x = 172$

Accepted Answer

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

Question 14

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = \frac { 3 \pi } { 7 }$

Accepted Answer

A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { 3 \pi } { 7 }$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { 3 \pi } { 7 }$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { 3 \pi } { 7 }$    
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { 3 \pi } { 7 }$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { 3 \pi } { 7 }$   
A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { 3 \pi } { 7 }$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { 3 \pi } { 7 }$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { 3 \pi } { 7 }$    
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { 3 \pi } { 7 }$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { 3 \pi } { 7 }$

Question 15

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.  $22 x ^ { 2 } - 13 x - 200 y - 112 = 0$

Accepted Answer

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

Question 16

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0.  $( - 7,7 )$

Accepted Answer

A) Polar coordinates: $\left( - \sqrt { 7 } , \frac { \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( \sqrt { 98 } , \frac { 3 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( \sqrt { 98 } , - \frac { 3 \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( - \sqrt { 98 } , \frac { 3 \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 7 } , \frac { \pi } { 4 } \right)$ 
A) Polar coordinates: $\left( - \sqrt { 7 } , \frac { \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( \sqrt { 98 } , \frac { 3 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( \sqrt { 98 } , - \frac { 3 \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( - \sqrt { 98 } , \frac { 3 \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 7 } , \frac { \pi } { 4 } \right)$

Question 17

Sketch the graph of the ellipse, using the lateral recta.  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$

Accepted Answer

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

Question 18

Find the vertex and directrix of the parabola. $x ^ { 2 } - 14 x - 8 y + 73 = 0$

Accepted Answer

A) vertex: $( 7,3 )$ directrix: $y = 5$ 
B) vertex: $( - 7 , - 3 )$ directrix: $y = 5$ 
C) vertex: $( 7,3 )$ directrix: $y = 1$ 
D) vertex: $( - 7 , - 3 )$ directrix: $y = - 5$ 
E) vertex: $( - 7 , - 3 )$ directrix: $y = 9$ 
A) vertex: $( 7,3 )$ directrix: $y = 5$ 
B) vertex: $( - 7 , - 3 )$ directrix: $y = 5$ 
C) vertex: $( 7,3 )$ directrix: $y = 1$ 
D) vertex: $( - 7 , - 3 )$ directrix: $y = - 5$ 
E) vertex: $( - 7 , - 3 )$ directrix: $y = 9$

Question 19

Find the center and vertices of the hyperbola. $12 x ^ { 2 } - 4 y ^ { 2 } - 48 x + 32 y - 64 = 0$

Accepted Answer

A) center: (-2, -4), vertices: (-2, -6), (-2, -2) 
B) center: (2, 4), vertices: (2, 2), (2, 6) 
C) center: (2, 4), vertices: (0, 4), (4, 4) 
D) center: (-2, -4), vertices: (-4, -4), (0, -4) 
E) center: (-4, -2), vertices: (-6, -2), (-2, -2) 
A) center: (-2, -4), vertices: (-2, -6), (-2, -2) 
B) center: (2, 4), vertices: (2, 2), (2, 6) 
C) center: (2, 4), vertices: (0, 4), (4, 4) 
D) center: (-2, -4), vertices: (-4, -4), (0, -4) 
E) center: (-4, -2), vertices: (-6, -2), (-2, -2)

Question 20

By using a graphing utility select the correct graph of the polar equation.Identify the graph.  $\frac { - 3 } { 2 + 8 \sin \theta }$

Accepted Answer

A)    $e = 4 > 1 \Rightarrow$ Hyperbola 
B)    $e = 4 > 1 \Rightarrow$ Hyperbola 
C)    $e = 4 > 1 \Rightarrow$ Hyperbola 
D)   $e = 4 > 1 \Rightarrow$ Hyperbola 
E)    $e = 4 > 1 \Rightarrow$ Hyperbola 
A)    $e = 4 > 1 \Rightarrow$ Hyperbola 
B)    $e = 4 > 1 \Rightarrow$ Hyperbola 
C)    $e = 4 > 1 \Rightarrow$ Hyperbola 
D)   $e = 4 > 1 \Rightarrow$ Hyperbola 
E)    $e = 4 > 1 \Rightarrow$ Hyperbola

Select correct graph to graph rotated conic. $r = \frac { 6 } { 6 + \sin ( \theta - \pi / 3 ) }$

Find the angle $\theta$ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. 12x+6y=18 3x-2y=-1

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: $( \pm 4,0 )$ ; foci: $( \pm 8,0 )$

Use the Quadratic Formula to solve for $y$ . $x ^ { 2 } - 12 x y - 10 y ^ { 2 } - 22 = 0$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±2); asymptotes: y = ± $\frac { 3 } { 2 }$ x

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 5 \cos 2 \theta$

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

Find the center and vertices of the hyperbola and sketch its graph, using asymptotes as sketching aids. $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=4\theta y=2\theta

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 1 } { 7 } x$

The $x ^ { \prime } y ^ { \prime }$ -coordinate system has been rotated $\theta$ degrees from the $x y$ -coordinate system.The coordinates of a point in the $x y$ -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. $\theta = 30 ^ { \circ }$ , $( 2,6 )$

Graph the hyperbola. $9 y ^ { 2 } - 16 x ^ { 2 } + 36 y + 64 x = 172$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = \frac { 3 \pi } { 7 }$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $22 x ^ { 2 } - 13 x - 200 y - 112 = 0$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( - 7,7 )$

Sketch the graph of the ellipse, using the lateral recta. $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$

Find the vertex and directrix of the parabola. $x ^ { 2 } - 14 x - 8 y + 73 = 0$

Find the center and vertices of the hyperbola. $12 x ^ { 2 } - 4 y ^ { 2 } - 48 x + 32 y - 64 = 0$

By using a graphing utility select the correct graph of the polar equation.Identify the graph. $\frac { - 3 } { 2 + 8 \sin \theta }$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

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Analytic Geometry In Three Dimensions

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Exam 10: Topics In Analytic Geometry

Select correct graph to graph rotated conic. r=66+sin⁡(θ−π/3)r = \frac { 6 } { 6 + \sin ( \theta - \pi / 3 ) }r=6+sin(θ−π/3)6​

Find the angle θ\thetaθ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. 12x+6y=18 3x-2y=-1

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±4,0)( \pm 4,0 )(±4,0) ; foci: (±8,0)( \pm 8,0 )(±8,0)

Use the Quadratic Formula to solve for yyy . x2−12xy−10y2−22=0x ^ { 2 } - 12 x y - 10 y ^ { 2 } - 22 = 0x2−12xy−10y2−22=0

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±2); asymptotes: y = ± 32\frac { 3 } { 2 }23​ x

Find the angle θ\thetaθ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. x-y=0 5x-4y=-3

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=5cos⁡2θr = 5 \cos 2 \thetar=5cos2θ

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

Find the center and vertices of the hyperbola and sketch its graph, using asymptotes as sketching aids. x29−y225=1\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 19x2​−25y2​=1

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=4\theta y=2\theta

Find the vertex and focus of the parabola. y2=−17xy ^ { 2 } = - \frac { 1 } { 7 } xy2=−71​x

Graph the hyperbola. 9y2−16x2+36y+64x=1729 y ^ { 2 } - 16 x ^ { 2 } + 36 y + 64 x = 1729y2−16x2+36y+64x=172

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=3π7r = \frac { 3 \pi } { 7 }r=73π​

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 22x2−13x−200y−112=022 x ^ { 2 } - 13 x - 200 y - 112 = 022x2−13x−200y−112=0

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. (−7,7)( - 7,7 )(−7,7)

Sketch the graph of the ellipse, using the lateral recta. x24+y216=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 14x2​+16y2​=1

Find the vertex and directrix of the parabola. x2−14x−8y+73=0x ^ { 2 } - 14 x - 8 y + 73 = 0x2−14x−8y+73=0

Find the center and vertices of the hyperbola. 12x2−4y2−48x+32y−64=012 x ^ { 2 } - 4 y ^ { 2 } - 48 x + 32 y - 64 = 012x2−4y2−48x+32y−64=0

By using a graphing utility select the correct graph of the polar equation.Identify the graph. −32+8sin⁡θ\frac { - 3 } { 2 + 8 \sin \theta }2+8sinθ−3​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Select correct graph to graph rotated conic. $r = \frac { 6 } { 6 + \sin ( \theta - \pi / 3 ) }$

Find the angle $\theta$ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. 12x+6y=18 3x-2y=-1

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: $( \pm 4,0 )$ ; foci: $( \pm 8,0 )$

Use the Quadratic Formula to solve for $y$ . $x ^ { 2 } - 12 x y - 10 y ^ { 2 } - 22 = 0$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±2); asymptotes: y = ± $\frac { 3 } { 2 }$ x

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 5 \cos 2 \theta$

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

Find the center and vertices of the hyperbola and sketch its graph, using asymptotes as sketching aids. $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 1 } { 7 } x$

Graph the hyperbola. $9 y ^ { 2 } - 16 x ^ { 2 } + 36 y + 64 x = 172$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = \frac { 3 \pi } { 7 }$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $22 x ^ { 2 } - 13 x - 200 y - 112 = 0$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( - 7,7 )$

Sketch the graph of the ellipse, using the lateral recta. $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$

Find the vertex and directrix of the parabola. $x ^ { 2 } - 14 x - 8 y + 73 = 0$

Find the center and vertices of the hyperbola. $12 x ^ { 2 } - 4 y ^ { 2 } - 48 x + 32 y - 64 = 0$

By using a graphing utility select the correct graph of the polar equation.Identify the graph. $\frac { - 3 } { 2 + 8 \sin \theta }$