Question 1

Select the polar equation of graph.

Accepted Answer

A)  $\frac { 8 } { 6 - \sin \theta }$ 
B)  $\frac { 8 } { 6 - \cos \theta }$ 
C)  $\frac { 1 } { 6 + \cos \theta }$ 
D)  $\frac { 8 } { 6 + \sin \theta }$ 
E)  $\frac { 8 } { 6 + \cos \theta }$ 
A)  $\frac { 8 } { 6 - \sin \theta }$ 
B)  $\frac { 8 } { 6 - \cos \theta }$ 
C)  $\frac { 1 } { 6 + \cos \theta }$ 
D)  $\frac { 8 } { 6 + \sin \theta }$ 
E)  $\frac { 8 } { 6 + \cos \theta }$

Question 2

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.  $\theta = 30 ^ { \circ }$ , $( 1,3 )$

Accepted Answer

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

Question 3

Find the standard form of the equation of the ellipse with the following characteristics. 
Foci: $( \pm 2,0 )$ , major axis of length: 22

Accepted Answer

A)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 117 } = 1$ 
B)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 480 } = 1$ 
E)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 121 } = 1$ 
A)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 117 } = 1$ 
B)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 480 } = 1$ 
E)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 121 } = 1$

Question 4

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.  $$\begin{array} { l } 
4 x - 4 y = 4 \
5 x + 4 y = 7
\end{array}$$

Accepted Answer

A)  $\Theta \approx 1.4601 \text { radians } \approx 83.7 ^ { \circ }$ 
B)  $\Theta \approx 1.4601 \text { radians } \approx 82.7 ^ { \circ }$ 
C)  $\Theta \approx 1.4601 \text { radians } \approx 84.7 ^ { \circ }$ 
D)  $\Theta \approx 1.4601 \text { radians } \approx 85.7 ^ { \circ }$ 
E)  $\Theta \approx 1.4601 \text { radians } \approx 81.7 ^ { \circ }$ 
A)  $\Theta \approx 1.4601 \text { radians } \approx 83.7 ^ { \circ }$ 
B)  $\Theta \approx 1.4601 \text { radians } \approx 82.7 ^ { \circ }$ 
C)  $\Theta \approx 1.4601 \text { radians } \approx 84.7 ^ { \circ }$ 
D)  $\Theta \approx 1.4601 \text { radians } \approx 85.7 ^ { \circ }$ 
E)  $\Theta \approx 1.4601 \text { radians } \approx 81.7 ^ { \circ }$

Question 5

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.  $7 x + 5 y = 0$

Accepted Answer

A)  $\Theta \approx 2.2318 \text { radians } \approx 127.9 ^ { \circ }$ 
B)  $\theta \approx 2.2318 \text { radians } \approx 128.9 ^ { \circ }$ 
C)  $\theta \approx 2.2318 \text { radians } \approx 126.9 ^ { \circ }$ 
D)  $\theta \approx 2.2318 \text { radians } \approx 129.9 ^ { \circ }$ 
E)  $\theta \approx 2.2318 \text { radians } \approx 125.9 ^ { \circ }$ 
A)  $\Theta \approx 2.2318 \text { radians } \approx 127.9 ^ { \circ }$ 
B)  $\theta \approx 2.2318 \text { radians } \approx 128.9 ^ { \circ }$ 
C)  $\theta \approx 2.2318 \text { radians } \approx 126.9 ^ { \circ }$ 
D)  $\theta \approx 2.2318 \text { radians } \approx 129.9 ^ { \circ }$ 
E)  $\theta \approx 2.2318 \text { radians } \approx 125.9 ^ { \circ }$

Question 6

Give the coordinates of the circle's center and its radius.  $x ^ { 2 } + y ^ { 2 } - 64 = 0$

Accepted Answer

A) (1, 1); r = 64 
B) (0, 0); r = 8 
C) (1, 1); r = 8 
D) (0, 0); r = 64 
E) none of these 
A) (1, 1); r = 64 
B) (0, 0); r = 8 
C) (1, 1); r = 8 
D) (0, 0); r = 64 
E) none of these

Question 7

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = 4 - 6 \cos \theta$

Accepted Answer

A) Symmetric with respect to the polar axis $| r | = 10$ when $\theta = \pi$
$$r = 0 \text { when } \cos \theta = \frac { 4 } { 6 }$$    
B) Symmetric with respect to the polar axis $| r | = 10$ when $\theta = \pi$
$$r = 0 \text { when } \cos \theta = \frac { 4 } { 6 }$$    
C) Symmetric with respect to the polar axis $\begin{array} { l } 
| r | = 10 \text { when } \theta = \pi \
r = 0 \text { when } \cos \theta = \frac { 4 } { 6 }
\end{array}$    
D) Symmetric with respect to the polar axis $| r | = 10$ when $\theta = \pi$
$$r = 0 \text { when } \cos \theta = \frac { 4 } { 6 }$$    
E) Symmetric with respect to the polar axis $| r | = 10$ when $\theta = \pi$
$$r = 0 \text { when } \cos \theta = \frac { 4 } { 6 }$$    
A) Symmetric with respect to the polar axis $| r | = 10$ when $\theta = \pi$
$$r = 0 \text { when } \cos \theta = \frac { 4 } { 6 }$$    
B) Symmetric with respect to the polar axis $| r | = 10$ when $\theta = \pi$
$$r = 0 \text { when } \cos \theta = \frac { 4 } { 6 }$$    
C) Symmetric with respect to the polar axis $\begin{array} { l } 
| r | = 10 \text { when } \theta = \pi \
r = 0 \text { when } \cos \theta = \frac { 4 } { 6 }
\end{array}$    
D) Symmetric with respect to the polar axis $| r | = 10$ when $\theta = \pi$
$$r = 0 \text { when } \cos \theta = \frac { 4 } { 6 }$$    
E) Symmetric with respect to the polar axis $| r | = 10$ when $\theta = \pi$
$$r = 0 \text { when } \cos \theta = \frac { 4 } { 6 }$$

Question 8

An elliptical stained-glass insert is to be fitted in a 6ft by 4 ft rectangular opening (see figure).Using the coordinate system shown, find an equation for the ellipse.

Accepted Answer

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

Question 9

Identify the conic and select its correct graph.  $r = \frac { 8 } { 1 + \sin \theta }$

Accepted Answer

A)  $e = 1 \Rightarrow$ Parabola   
B)  $e = 1 \Rightarrow$ P  
C)  $e = 2 \Rightarrow$ Hyperbola   
D)  $e = 1 \Rightarrow$ Parabola   
E)  $e = 1 \Rightarrow$ Parabola   
A)  $e = 1 \Rightarrow$ Parabola   
B)  $e = 1 \Rightarrow$ P  
C)  $e = 2 \Rightarrow$ Hyperbola   
D)  $e = 1 \Rightarrow$ Parabola   
E)  $e = 1 \Rightarrow$ Parabola

Question 10

Find the center and foci of the hyperbola. $\frac { ( y - 8 ) ^ { 2 } } { 9 } - \frac { ( x + 5 ) ^ { 2 } } { 27 } = 1$

Accepted Answer

A) center: (-5, 8), foci: (-11, 8), (1, 8) 
B) center: (-5, 8), foci: (-5, 2), (-5, 14) 
C) center: (-8, 5), foci: (-8, -1), (-8, 11) 
D) center: (8, -5), foci: (2, -5), (14, -5) 
E) center: (5, -8), foci: (5, -14), (5, -2) 
A) center: (-5, 8), foci: (-11, 8), (1, 8) 
B) center: (-5, 8), foci: (-5, 2), (-5, 14) 
C) center: (-8, 5), foci: (-8, -1), (-8, 11) 
D) center: (8, -5), foci: (2, -5), (14, -5) 
E) center: (5, -8), foci: (5, -14), (5, -2)

Question 11

Identify the conic and select its correct graph. $r = \frac { 1 } { - 1 + 2 \cos \theta }$

Accepted Answer

A)  $e = 2 > 1 \Rightarrow$ Hyperbola   
B)  $e = 2 > 1 \Rightarrow$ H  
C)  $e = 2 > 1 \Rightarrow$ H  
D)  $e = 2 > 1 \Rightarrow$ H  
E)  $e = - 2 > 1 \Rightarrow$ Hyperbola   
A)  $e = 2 > 1 \Rightarrow$ Hyperbola   
B)  $e = 2 > 1 \Rightarrow$ H  
C)  $e = 2 > 1 \Rightarrow$ H  
D)  $e = 2 > 1 \Rightarrow$ H  
E)  $e = - 2 > 1 \Rightarrow$ Hyperbola

Question 12

Find the eccentricity of the ellipse.  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = 1$

Accepted Answer

A) Eccentricity: $e = \frac { 8 \sqrt { 17 } } { 17 }$ 
B) Eccentricity: $e = \frac { \sqrt { 17 } } { 9 }$ 
C) Eccentricity: $e = - \frac { \sqrt { 17 } } { 9 }$ 
D) Eccentricity: $e = \frac { \sqrt { 17 } } { 17 }$ 
E) Eccentricity: $e = - \frac { 9 \sqrt { 17 } } { 9 }$ 
A) Eccentricity: $e = \frac { 8 \sqrt { 17 } } { 17 }$ 
B) Eccentricity: $e = \frac { \sqrt { 17 } } { 9 }$ 
C) Eccentricity: $e = - \frac { \sqrt { 17 } } { 9 }$ 
D) Eccentricity: $e = \frac { \sqrt { 17 } } { 17 }$ 
E) Eccentricity: $e = - \frac { 9 \sqrt { 17 } } { 9 }$

Question 13

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = 4 + 6 \sin \theta$

Accepted Answer

A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 10$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \theta = \frac { 11 \pi } { 6 }$   
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 10$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \theta = \frac { 11 \pi } { 6 }$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 10$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \theta = \frac { 11 \pi } { 6 }$   
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 10$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \theta = \frac { 11 \pi } { 6 }$   
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 10$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \theta = \frac { 11 \pi } { 6 }$    
A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 10$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \theta = \frac { 11 \pi } { 6 }$   
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 10$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \theta = \frac { 11 \pi } { 6 }$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 10$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \theta = \frac { 11 \pi } { 6 }$   
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 10$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \theta = \frac { 11 \pi } { 6 }$   
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 10$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \theta = \frac { 11 \pi } { 6 }$

Question 14

Use a graphing utility to graph the parabola.  $x + 5 = 4 ( y - 3 ) ^ { 2 }$

Accepted Answer

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

Question 15

Select the graph of the following equation.  $x ^ { 2 } = 8 y$

Accepted Answer

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

Question 16

Use the discriminant to classify the graph.  $x ^ { 2 } - 10 x y - 9 y ^ { 2 } + 8 x - 33 = 0$

Accepted Answer

A) The graph is a ellipse. 
B) The graph is a circle. 
C) The graph is a hyperbola. 
D) The graph is a line. 
E) The graph is a parabola. 
A) The graph is a ellipse. 
B) The graph is a circle. 
C) The graph is a hyperbola. 
D) The graph is a line. 
E) The graph is a parabola.

Question 17

Use a graphing utility to graph the conic. $x ^ { 2 } - 4 x y + 2 y ^ { 2 } = 8$

Accepted Answer

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

Question 18

Select the graph for following equation.  $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1$

Accepted Answer

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

Question 19

The Falls Incline Railway in Niagara Falls, Ontario, Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 180 feet long with a 42% uphill grade (see figure).Select the graph of the equation of the line that models the railway track.    $$a = 180$$

Accepted Answer

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

Question 20

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

Accepted Answer

A) y2 = 20x 
B) y2 = -5x 
C) x2 = -20y 
D) x2 = -5y 
E) x2 = 20y 
A) y2 = 20x 
B) y2 = -5x 
C) x2 = -20y 
D) x2 = -5y 
E) x2 = 20y

Select the polar equation of graph.

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. $\theta = 30 ^ { \circ }$ , $( 1,3 )$

Find the standard form of the equation of the ellipse with the following characteristics. Foci: $( \pm 2,0 )$ , major axis of length: 22

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $7 x + 5 y = 0$

Give the coordinates of the circle's center and its radius. $x ^ { 2 } + y ^ { 2 } - 64 = 0$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 4 - 6 \cos \theta$

An elliptical stained-glass insert is to be fitted in a 6ft by 4 ft rectangular opening (see figure).Using the coordinate system shown, find an equation for the ellipse.

Identify the conic and select its correct graph. $r = \frac { 8 } { 1 + \sin \theta }$

Find the center and foci of the hyperbola. $\frac { ( y - 8 ) ^ { 2 } } { 9 } - \frac { ( x + 5 ) ^ { 2 } } { 27 } = 1$

Identify the conic and select its correct graph. $r = \frac { 1 } { - 1 + 2 \cos \theta }$

Find the eccentricity of the ellipse. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = 1$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 4 + 6 \sin \theta$

Use a graphing utility to graph the parabola. $x + 5 = 4 ( y - 3 ) ^ { 2 }$

Select the graph of the following equation. $x ^ { 2 } = 8 y$

Use the discriminant to classify the graph. $x ^ { 2 } - 10 x y - 9 y ^ { 2 } + 8 x - 33 = 0$

Use a graphing utility to graph the conic. $x ^ { 2 } - 4 x y + 2 y ^ { 2 } = 8$

Select the graph for following equation. $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1$

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

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

Exam 10: Topics In Analytic Geometry

Select the polar equation of graph.

Find the standard form of the equation of the ellipse with the following characteristics. Foci: (±2,0)( \pm 2,0 )(±2,0) , major axis of length: 22

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. 4x-4y=4 5x+4y=7

Find the inclination θ\thetaθ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. 7x+5y=07 x + 5 y = 07x+5y=0

Give the coordinates of the circle's center and its radius. x2+y2−64=0x ^ { 2 } + y ^ { 2 } - 64 = 0x2+y2−64=0

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=4−6cos⁡θr = 4 - 6 \cos \thetar=4−6cosθ

An elliptical stained-glass insert is to be fitted in a 6ft by 4 ft rectangular opening (see figure).Using the coordinate system shown, find an equation for the ellipse.

Identify the conic and select its correct graph. r=81+sin⁡θr = \frac { 8 } { 1 + \sin \theta }r=1+sinθ8​

Find the center and foci of the hyperbola. (y−8)29−(x+5)227=1\frac { ( y - 8 ) ^ { 2 } } { 9 } - \frac { ( x + 5 ) ^ { 2 } } { 27 } = 19(y−8)2​−27(x+5)2​=1

Identify the conic and select its correct graph. r=1−1+2cos⁡θr = \frac { 1 } { - 1 + 2 \cos \theta }r=−1+2cosθ1​

Find the eccentricity of the ellipse. x264+y281=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = 164x2​+81y2​=1

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=4+6sin⁡θr = 4 + 6 \sin \thetar=4+6sinθ

Use a graphing utility to graph the parabola. x+5=4(y−3)2x + 5 = 4 ( y - 3 ) ^ { 2 }x+5=4(y−3)2

Select the graph of the following equation. x2=8yx ^ { 2 } = 8 yx2=8y

Use the discriminant to classify the graph. x2−10xy−9y2+8x−33=0x ^ { 2 } - 10 x y - 9 y ^ { 2 } + 8 x - 33 = 0x2−10xy−9y2+8x−33=0

Use a graphing utility to graph the conic. x2−4xy+2y2=8x ^ { 2 } - 4 x y + 2 y ^ { 2 } = 8x2−4xy+2y2=8

Select the graph for following equation. (x+2)29+(y+2)24=1\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 19(x+2)2​+4(y+2)2​=1

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

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

Find the standard form of the equation of the ellipse with the following characteristics. Foci: $( \pm 2,0 )$ , major axis of length: 22

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $7 x + 5 y = 0$

Give the coordinates of the circle's center and its radius. $x ^ { 2 } + y ^ { 2 } - 64 = 0$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 4 - 6 \cos \theta$

Identify the conic and select its correct graph. $r = \frac { 8 } { 1 + \sin \theta }$

Find the center and foci of the hyperbola. $\frac { ( y - 8 ) ^ { 2 } } { 9 } - \frac { ( x + 5 ) ^ { 2 } } { 27 } = 1$

Identify the conic and select its correct graph. $r = \frac { 1 } { - 1 + 2 \cos \theta }$

Find the eccentricity of the ellipse. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = 1$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 4 + 6 \sin \theta$

Use a graphing utility to graph the parabola. $x + 5 = 4 ( y - 3 ) ^ { 2 }$

Select the graph of the following equation. $x ^ { 2 } = 8 y$

Use the discriminant to classify the graph. $x ^ { 2 } - 10 x y - 9 y ^ { 2 } + 8 x - 33 = 0$

Use a graphing utility to graph the conic. $x ^ { 2 } - 4 x y + 2 y ^ { 2 } = 8$

Select the graph for following equation. $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1$

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