Question 1

Convert the rectangular equation to polar form.Assume a > 0, r > 1.  $x ^ { 2 } + y ^ { 2 } - 3 a y = 0$

Accepted Answer

A)  $r = 3 a \sin \theta$ 
B)  $r = 3 a \cot \Theta$ 
C)  $r = 3 a \cos \theta$ 
D)  $r = 3 \operatorname { asec } \theta$ 
E)  $r = 3 \operatorname { acsc } \theta$ 
A)  $r = 3 a \sin \theta$ 
B)  $r = 3 a \cot \Theta$ 
C)  $r = 3 a \cos \theta$ 
D)  $r = 3 \operatorname { asec } \theta$ 
E)  $r = 3 \operatorname { acsc } \theta$

Question 2

Find the distance between the point and the line.Round your answer to four decimal places.  Point Line
$( 7,5 ) \quad x - y = 50$

Accepted Answer

A)  $d \approx 24.3345$ 
B)  $d \approx 25.3345$ 
C)  $d \approx 23.3345$ 
D)  $d \approx 22.3345$ 
E)  $d \approx 26.3345$ 
A)  $d \approx 24.3345$ 
B)  $d \approx 25.3345$ 
C)  $d \approx 23.3345$ 
D)  $d \approx 22.3345$ 
E)  $d \approx 26.3345$

Question 3

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0.  $( 2,0 )$

Accepted Answer

A) Polar coordinates: $( 0 , - 2 )$ 
B) Polar coordinates: $( 0,2 )$ 
C) Polar coordinates: $( - 2,2 )$ 
D) Polar coordinates: $( - 2,0 )$ 
E) Polar coordinates: $( 2,0 )$ 
A) Polar coordinates: $( 0 , - 2 )$ 
B) Polar coordinates: $( 0,2 )$ 
C) Polar coordinates: $( - 2,2 )$ 
D) Polar coordinates: $( - 2,0 )$ 
E) Polar coordinates: $( 2,0 )$

Question 4

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

Accepted Answer

A)  $y = 1 \Rightarrow \text { Line }$   
B)  $y = 1 \Rightarrow \text { Line }$   
C)  $y = 1 \Rightarrow \text { Line }$   
D)  $y = 1 \Rightarrow \text { Line }$   
E)  $y = 1 \Rightarrow \text { Line }$   
A)  $y = 1 \Rightarrow \text { Line }$   
B)  $y = 1 \Rightarrow \text { Line }$   
C)  $y = 1 \Rightarrow \text { Line }$   
D)  $y = 1 \Rightarrow \text { Line }$   
E)  $y = 1 \Rightarrow \text { Line }$

Question 5

By using a graphing utility select the correct graph of the polar equation.  $\frac { - 3 } { 1 - \sin \theta }$

Accepted Answer

A)   $e = 1 \Rightarrow \text { Parabola }$ 
B)   $e = 1 \Rightarrow \text { Parabola }$ 
C)   $e = 1 \Rightarrow \text { Parabola }$ 
D)    $e = 1 \Rightarrow \text { Parabola }$ 
E)    $e = 1 \Rightarrow \text { Parabola }$ 
A)   $e = 1 \Rightarrow \text { Parabola }$ 
B)   $e = 1 \Rightarrow \text { Parabola }$ 
C)   $e = 1 \Rightarrow \text { Parabola }$ 
D)    $e = 1 \Rightarrow \text { Parabola }$ 
E)    $e = 1 \Rightarrow \text { Parabola }$

Question 6

Using following result find a set of parametric equation of conic. 
Circle: $x = h + r \cos \theta , y = k + r \sin \theta$ 
Circle: center: $( 8 , - 3 )$ ; radius: 5

Accepted Answer

A)  $x = 5 + 3 \cos \theta , y = 8 - 3 \sin \theta$ 
B)  $x = 3 + 5 \cos \theta , y = 8 - 5 \sin \theta$ 
C)  $x = 8 + 5 \cos \theta , y = 3 - 5 \sin \theta$ 
D)  $x = 8 - 5 \cos \theta , y = 3 + 5 \sin \theta$ 
E)  $x = 8 + 5 \cos \theta , y = - 3 + 5 \sin \theta$ 
A)  $x = 5 + 3 \cos \theta , y = 8 - 3 \sin \theta$ 
B)  $x = 3 + 5 \cos \theta , y = 8 - 5 \sin \theta$ 
C)  $x = 8 + 5 \cos \theta , y = 3 - 5 \sin \theta$ 
D)  $x = 8 - 5 \cos \theta , y = 3 + 5 \sin \theta$ 
E)  $x = 8 + 5 \cos \theta , y = - 3 + 5 \sin \theta$

Question 7

Find the standard form of the equation of the ellipse with the following graph.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 0$ , $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 0$ , $x ^ { 2 } + \frac { y ^ { 2 } } { 16 } = 0$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 100$ , $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$ , $x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $25 x ^ { 2 } + 4 y ^ { 2 } = 1$ , $\frac { x ^ { 2 } } { 2 } - \frac { y ^ { 2 } } { 36 } = 1$ , $\frac { x ^ { 2 } } { 16 } - y ^ { 2 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$ , $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 1$ , $x ^ { 2 } + \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } = 1$ , $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 36 } = 1$ , $\frac { x ^ { 2 } } { 16 } + y ^ { 2 } = 1$ 
A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 0$ , $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 0$ , $x ^ { 2 } + \frac { y ^ { 2 } } { 16 } = 0$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 100$ , $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$ , $x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $25 x ^ { 2 } + 4 y ^ { 2 } = 1$ , $\frac { x ^ { 2 } } { 2 } - \frac { y ^ { 2 } } { 36 } = 1$ , $\frac { x ^ { 2 } } { 16 } - y ^ { 2 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$ , $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 1$ , $x ^ { 2 } + \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } = 1$ , $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 36 } = 1$ , $\frac { x ^ { 2 } } { 16 } + y ^ { 2 } = 1$

Question 8

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = 3 + 7 \cos \theta$

Accepted Answer

A) Symmetric with respect to the polar axis $| r | = 10 \text { when } \theta = 0$   
B) Symmetric with respect to the polar axis $| r | = 10 \text { when } \theta = 0$    
C) Symmetric with respect to the polar axis $| r | = 10 \text { when } \theta = 0$    
D) Symmetric with respect to the polar axis $| r | = 10 \text { when } \theta = 0$    
E) Symmetric with respect to the polar axis $| r | = 10 \text { when } \theta = 0$    
A) Symmetric with respect to the polar axis $| r | = 10 \text { when } \theta = 0$   
B) Symmetric with respect to the polar axis $| r | = 10 \text { when } \theta = 0$    
C) Symmetric with respect to the polar axis $| r | = 10 \text { when } \theta = 0$    
D) Symmetric with respect to the polar axis $| r | = 10 \text { when } \theta = 0$    
E) Symmetric with respect to the polar axis $| r | = 10 \text { when } \theta = 0$

Question 9

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 49 } = 1$

Accepted Answer

A) Center: (0,0)Vertices: (±10,0)   
B) Center: (0,0)Vertices: (10,0)   
C) Center: (0,0)Vertices: (-10,0)   
D) Center: (0,0)Vertices: (-10,0)   
E) Center: (0,0)Vertices: (±10,0)   
A) Center: (0,0)Vertices: (±10,0)   
B) Center: (0,0)Vertices: (10,0)   
C) Center: (0,0)Vertices: (-10,0)   
D) Center: (0,0)Vertices: (-10,0)   
E) Center: (0,0)Vertices: (±10,0)

Question 10

Convert the rectangular equation to polar form.Assume r > 1.  $x ^ { 2 } + y ^ { 2 } = 49$

Accepted Answer

A)  $r = 7$ 
B)  $r = - 7$ 
C)  $r = \frac { 1 } { 7 }$ 
D)  $r = 49$ 
E)  $r = - \frac { 1 } { 7 }$ 
A)  $r = 7$ 
B)  $r = - 7$ 
C)  $r = \frac { 1 } { 7 }$ 
D)  $r = 49$ 
E)  $r = - \frac { 1 } { 7 }$

Question 11

Find the inclination  (in degrees) of the line with a slope of m.Round your answer to one decimal places.  $m = 0.6666666667$

Accepted Answer

A)  $\Theta \approx 35.7 ^ { \circ }$ 
B)  $\Theta \approx 34.7 ^ { \circ }$ 
C)  $\Theta \approx 33.7 ^ { \circ }$ 
D)  $\Theta \approx 32.7 ^ { \circ }$ 
E)  $\Theta \approx 31.7 ^ { \circ }$ 
A)  $\Theta \approx 35.7 ^ { \circ }$ 
B)  $\Theta \approx 34.7 ^ { \circ }$ 
C)  $\Theta \approx 33.7 ^ { \circ }$ 
D)  $\Theta \approx 32.7 ^ { \circ }$ 
E)  $\Theta \approx 31.7 ^ { \circ }$

Question 12

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. 
Vertices: (0,±3); focies: (0,±7)

Accepted Answer

A)  $- \frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$ 
B)  $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 40 } = 1$ 
D)  $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = - 1$ 
E)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$ 
A)  $- \frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$ 
B)  $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 40 } = 1$ 
D)  $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = - 1$ 
E)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$

Question 13

By using a graphing utility select the correct graph of the polar equation.Identify the graph.  $\frac { 12 } { 2 - \cos \theta }$

Accepted Answer

A)   $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse 
B)    $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse 
C)    $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse 
D)    $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse 
E)    $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse 
A)   $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse 
B)    $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse 
C)    $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse 
D)    $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse 
E)    $e = \frac { 1 } { 2 } < 1 \Rightarrow$ Ellipse

Question 14

Use the discriminant to classify the graph.  $x ^ { 2 } + 6 x y + 9 y ^ { 2 } - 5 x - y - 3 = 0$

Accepted Answer

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

Question 15

Find the vertex and focus of the parabola. $x ^ { 2 } + 28 y = 0$

Accepted Answer

A) vertex: (-7 , 0) focus: (0, 0) 
B) vertex: (7, 0) focus: (0, 0) 
C) vertex: (0, 0) focus: (-7, 0) 
D) vertex: (0, 0) focus: (0, -7) 
E) vertex: (0, 0) focus: (0, 7) 
A) vertex: (-7 , 0) focus: (0, 0) 
B) vertex: (7, 0) focus: (0, 0) 
C) vertex: (0, 0) focus: (-7, 0) 
D) vertex: (0, 0) focus: (0, -7) 
E) vertex: (0, 0) focus: (0, 7)

Question 16

Select the curve represented by the parametric equations.  $\begin{array} { l } 
x = \frac { 2 } { 3 } t \
y = t ^ { 2 }
\end{array}$

Accepted Answer

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

Question 17

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. 
Focies: (±7,0); major axis of length 16

Accepted Answer

A)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 15 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 15 } = 1$ 
C)  $- \frac { x ^ { 2 } } { 15 } + \frac { y ^ { 2 } } { 64 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 15 } = - 1$ 
E)  $\frac { x ^ { 2 } } { 15 } + \frac { y ^ { 2 } } { 64 } = 1$ 
A)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 15 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 15 } = 1$ 
C)  $- \frac { x ^ { 2 } } { 15 } + \frac { y ^ { 2 } } { 64 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 15 } = - 1$ 
E)  $\frac { x ^ { 2 } } { 15 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 18

Select the graph of the following equation, showing both sets of axes.  $\frac { \left( y ^ { \prime } \right) ^ { 2 } } { 2 } - \frac { \left( x ^ { \prime } \right) ^ { 2 } } { 2 } = 1$

Accepted Answer

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

Question 19

Find the inclination  (in degrees) of the line with a slope of m.Round your answer to one decimal places.  $m = 2$

Accepted Answer

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

Question 20

Select the graph of the following equation: 
 $y ^ { 2 } = - 2 x$

Accepted Answer

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

Convert the rectangular equation to polar form.Assume a > 0, r > 1. $x ^ { 2 } + y ^ { 2 } - 3 a y = 0$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 7,5 ) \quad x - y = 50$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( 2,0 )$

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

By using a graphing utility select the correct graph of the polar equation. $\frac { - 3 } { 1 - \sin \theta }$

Using following result find a set of parametric equation of conic. Circle: $x = h + r \cos \theta , y = k + r \sin \theta$ Circle: center: $( 8 , - 3 )$ ; radius: 5

Find the standard form of the equation of the ellipse with the following graph.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 3 + 7 \cos \theta$

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 49 } = 1$

Convert the rectangular equation to polar form.Assume r > 1. $x ^ { 2 } + y ^ { 2 } = 49$

Find the inclination (in degrees) of the line with a slope of m.Round your answer to one decimal places. $m = 0.6666666667$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±3); focies: (0,±7)

By using a graphing utility select the correct graph of the polar equation.Identify the graph. $\frac { 12 } { 2 - \cos \theta }$

Use the discriminant to classify the graph. $x ^ { 2 } + 6 x y + 9 y ^ { 2 } - 5 x - y - 3 = 0$

Find the vertex and focus of the parabola. $x ^ { 2 } + 28 y = 0$

Select the curve represented by the parametric equations. x=t y=

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Focies: (±7,0); major axis of length 16

Select the graph of the following equation, showing both sets of axes. $\frac { \left( y ^ { \prime } \right) ^ { 2 } } { 2 } - \frac { \left( x ^ { \prime } \right) ^ { 2 } } { 2 } = 1$

Find the inclination (in degrees) of the line with a slope of m.Round your answer to one decimal places. $m = 2$

Select the graph of the following equation: $y ^ { 2 } = - 2 x$

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

Convert the rectangular equation to polar form.Assume a > 0, r > 1. x2+y2−3ay=0x ^ { 2 } + y ^ { 2 } - 3 a y = 0x2+y2−3ay=0

Find the distance between the point and the line.Round your answer to four decimal places. Point Line (7,5)x−y=50( 7,5 ) \quad x - y = 50(7,5)x−y=50

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. (2,0)( 2,0 )(2,0)

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

By using a graphing utility select the correct graph of the polar equation. −31−sin⁡θ\frac { - 3 } { 1 - \sin \theta }1−sinθ−3​

Using following result find a set of parametric equation of conic. Circle: x=h+rcos⁡θ,y=k+rsin⁡θx = h + r \cos \theta , y = k + r \sin \thetax=h+rcosθ,y=k+rsinθ Circle: center: (8,−3)( 8 , - 3 )(8,−3) ; radius: 5

Find the standard form of the equation of the ellipse with the following graph.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=3+7cos⁡θr = 3 + 7 \cos \thetar=3+7cosθ

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. x2100+y249=1\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 49 } = 1100x2​+49y2​=1

Convert the rectangular equation to polar form.Assume r > 1. x2+y2=49x ^ { 2 } + y ^ { 2 } = 49x2+y2=49

Find the inclination (in degrees) of the line with a slope of m.Round your answer to one decimal places. m=0.6666666667m = 0.6666666667m=0.6666666667

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±3); focies: (0,±7)

By using a graphing utility select the correct graph of the polar equation.Identify the graph. 122−cos⁡θ\frac { 12 } { 2 - \cos \theta }2−cosθ12​

Use the discriminant to classify the graph. x2+6xy+9y2−5x−y−3=0x ^ { 2 } + 6 x y + 9 y ^ { 2 } - 5 x - y - 3 = 0x2+6xy+9y2−5x−y−3=0

Find the vertex and focus of the parabola. x2+28y=0x ^ { 2 } + 28 y = 0x2+28y=0

Select the curve represented by the parametric equations. x=t y=

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Focies: (±7,0); major axis of length 16

Select the graph of the following equation, showing both sets of axes. (y′)22−(x′)22=1\frac { \left( y ^ { \prime } \right) ^ { 2 } } { 2 } - \frac { \left( x ^ { \prime } \right) ^ { 2 } } { 2 } = 12(y′)2​−2(x′)2​=1

Find the inclination (in degrees) of the line with a slope of m.Round your answer to one decimal places. m=2m = 2m=2

Select the graph of the following equation: y2=−2xy ^ { 2 } = - 2 xy2=−2x

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

Convert the rectangular equation to polar form.Assume a > 0, r > 1. $x ^ { 2 } + y ^ { 2 } - 3 a y = 0$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 7,5 ) \quad x - y = 50$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( 2,0 )$

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

By using a graphing utility select the correct graph of the polar equation. $\frac { - 3 } { 1 - \sin \theta }$

Using following result find a set of parametric equation of conic. Circle: $x = h + r \cos \theta , y = k + r \sin \theta$ Circle: center: $( 8 , - 3 )$ ; radius: 5

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 3 + 7 \cos \theta$

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 49 } = 1$

Convert the rectangular equation to polar form.Assume r > 1. $x ^ { 2 } + y ^ { 2 } = 49$

Find the inclination (in degrees) of the line with a slope of m.Round your answer to one decimal places. $m = 0.6666666667$

By using a graphing utility select the correct graph of the polar equation.Identify the graph. $\frac { 12 } { 2 - \cos \theta }$

Use the discriminant to classify the graph. $x ^ { 2 } + 6 x y + 9 y ^ { 2 } - 5 x - y - 3 = 0$

Find the vertex and focus of the parabola. $x ^ { 2 } + 28 y = 0$

Select the graph of the following equation, showing both sets of axes. $\frac { \left( y ^ { \prime } \right) ^ { 2 } } { 2 } - \frac { \left( x ^ { \prime } \right) ^ { 2 } } { 2 } = 1$

Find the inclination (in degrees) of the line with a slope of m.Round your answer to one decimal places. $m = 2$

Select the graph of the following equation: $y ^ { 2 } = - 2 x$