Question 1

Select the graph of degenerate conic.  $x ^ { 2 } + y ^ { 2 } - 2 x + 16 y + 65 = 0$

Accepted Answer

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

Question 2

Select the graph of $r = 3 \cos \theta$ over the interval.Describe the part of the graph obtained in this case.  $- \frac { \pi } { 2 } \leq \theta \leq \frac { \pi } { 2 }$

Accepted Answer

A)    Entire circle 
B)   Entire circle 
C)    Entire circle 
D)    Entire circle 
E)    Entire circle 
A)    Entire circle 
B)   Entire circle 
C)    Entire circle 
D)    Entire circle 
E)    Entire circle

Question 3

Find the center and vertices of the ellipse.  $x ^ { 2 } + 16 y ^ { 2 } - 10 x - 32 y + 25 = 0$

Accepted Answer

A) center: $( 1,5 )$ ; vertices: $( - 3,5 ) , ( 5,5 )$ 
B) center: $( 5,1 )$ ; vertices: $( 1,1 ) , ( 9,1 )$ 
C) center: $( - 5 , - 1 )$ ; vertices: $( - 6 , - 1 ) , ( - 4 , - 1 )$ 
D) center: $( - 5 , - 1 )$ ; vertices: $( - 9 , - 1 ) , ( 1 , - 1 )$ 
E) center: $( 5,1 )$ ; vertices: $( 4,1 ) , ( 6,1 )$ 
A) center: $( 1,5 )$ ; vertices: $( - 3,5 ) , ( 5,5 )$ 
B) center: $( 5,1 )$ ; vertices: $( 1,1 ) , ( 9,1 )$ 
C) center: $( - 5 , - 1 )$ ; vertices: $( - 6 , - 1 ) , ( - 4 , - 1 )$ 
D) center: $( - 5 , - 1 )$ ; vertices: $( - 9 , - 1 ) , ( 1 , - 1 )$ 
E) center: $( 5,1 )$ ; vertices: $( 4,1 ) , ( 6,1 )$

Question 4

Select the graph for following equation.  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Accepted Answer

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

Question 5

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.  $\begin{array} { l } 
0.04 x + 0.02 y = 0.06 \
0.07 x - 0.06 y = 0.05
\end{array}$

Accepted Answer

A)  $\theta \approx 1.1903 \text { radians } \approx 69.2 ^ { \circ }$ 
B)  $\theta \approx 1.1903 \text { radians } \approx 67.2 ^ { \circ }$ 
C)  $\theta \approx 1.1903 \text { radians } \approx 70.2 ^ { \circ }$ 
D)  $\theta \approx 1.1903 \text { radians } \approx 66.2 ^ { \circ }$ 
E)  $\theta \approx 1.1903 \text { radians } \approx 68.2 ^ { \circ }$ 
A)  $\theta \approx 1.1903 \text { radians } \approx 69.2 ^ { \circ }$ 
B)  $\theta \approx 1.1903 \text { radians } \approx 67.2 ^ { \circ }$ 
C)  $\theta \approx 1.1903 \text { radians } \approx 70.2 ^ { \circ }$ 
D)  $\theta \approx 1.1903 \text { radians } \approx 66.2 ^ { \circ }$ 
E)  $\theta \approx 1.1903 \text { radians } \approx 68.2 ^ { \circ }$

Question 6

Find the vertex, focus, and directrix of the parabola. $( x - 1 ) ^ { 2 } + 16 ( y + 6 ) = 0$

Accepted Answer

A) Vertex: $( 0 , - 4 )$ ; Focus: $( 1 , - 6 )$ ; Directrix: $y = 0$ 
B) Vertex: $( 1 , - 10 )$ ; Focus: $( 1 , - 10 )$ ; Directrix: $y = 0$ 
C) Vertex: $( - 4,1 )$ ; Focus: $( - 4,1 )$ ; Directrix: $y = 0$ 
D) Vertex: $( 1 , - 6 )$ ; Focus: $( 1 , - 10 )$ ; Directrix: $y = 0$ 
E) Vertex: $( 1 , - 6 )$ ; Focus: $( 1 , - 4 )$ ; Directrix: $y = 6$ 
A) Vertex: $( 0 , - 4 )$ ; Focus: $( 1 , - 6 )$ ; Directrix: $y = 0$ 
B) Vertex: $( 1 , - 10 )$ ; Focus: $( 1 , - 10 )$ ; Directrix: $y = 0$ 
C) Vertex: $( - 4,1 )$ ; Focus: $( - 4,1 )$ ; Directrix: $y = 0$ 
D) Vertex: $( 1 , - 6 )$ ; Focus: $( 1 , - 10 )$ ; Directrix: $y = 0$ 
E) Vertex: $( 1 , - 6 )$ ; Focus: $( 1 , - 4 )$ ; Directrix: $y = 6$

Question 7

Find the center, vertices and foci of the hyperbola.  $\frac { y ^ { 2 } } { 1 } - \frac { x ^ { 2 } } { 36 } = 1$

Accepted Answer

A) Center: (0, 0)Vertices: $( 0 , \pm 1 )$ Foci: $( 0 , \pm \sqrt { 37 } )$ 
B) Center: $( 36,1 )$ Vertices: $( 0 , \pm \sqrt { 37 } )$ Foci: $( 0 , \pm 1 )$ 
C) Center: (0, 0)Vertices: $( \pm 1,0 )$ Foci: $( \pm \sqrt { 37 } , 0 )$ 
D) Center: $( 36,1 )$ Vertices:   $( 0 , \pm 1 )$ Foci: $( 0 , \pm \sqrt { 37 } )$ 
E) Center: $( 36,1 )$ Vertices: $( \pm 1,0 )$ Foci: $( \pm \sqrt { 37 } , 0 )$ 
A) Center: (0, 0)Vertices: $( 0 , \pm 1 )$ Foci: $( 0 , \pm \sqrt { 37 } )$ 
B) Center: $( 36,1 )$ Vertices: $( 0 , \pm \sqrt { 37 } )$ Foci: $( 0 , \pm 1 )$ 
C) Center: (0, 0)Vertices: $( \pm 1,0 )$ Foci: $( \pm \sqrt { 37 } , 0 )$ 
D) Center: $( 36,1 )$ Vertices:   $( 0 , \pm 1 )$ Foci: $( 0 , \pm \sqrt { 37 } )$ 
E) Center: $( 36,1 )$ Vertices: $( \pm 1,0 )$ Foci: $( \pm \sqrt { 37 } , 0 )$

Question 8

A roof has a rise of 9 feet for every horizontal change of 11 feet (see figure).Find the inclination of the roof.Round your answers to one decimal place.     $a = 9 , b = 11$

Accepted Answer

A)  $\Theta \approx 39.3 ^ { \circ }$ 
B)  $\Theta \approx 40.3 ^ { \circ }$ 
C)  $\Theta \approx 41.3 ^ { \circ }$ 
D)  $\Theta \approx 38.3 ^ { \circ }$ 
E)  $\Theta \approx 37.3 ^ { \circ }$ 
A)  $\Theta \approx 39.3 ^ { \circ }$ 
B)  $\Theta \approx 40.3 ^ { \circ }$ 
C)  $\Theta \approx 41.3 ^ { \circ }$ 
D)  $\Theta \approx 38.3 ^ { \circ }$ 
E)  $\Theta \approx 37.3 ^ { \circ }$

Question 9

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.  $y ^ { 2 } - 4 x ^ { 2 } + 4 x - 8 y - 24 = 0$

Accepted Answer

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

Question 10

Write the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (5, 0).

Accepted Answer

The answer of Write the equation of the hyperbola with...

Question 11

Find the center and vertices which located on the major axis of the ellipse. $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$

Accepted Answer

A) center: (0, 0) vertices: (0, -5), (0, 5) 
B) center: (0, 0) vertices: (-3, 0), (3, 0) 
C) center: (5, 3) vertices: (-5, -3), (5, 3) 
D) center: (0, 0) vertices: (-5, 0), (5, 0) 
E) center: (5, 0) vertices: (0, -3), (0, 3) 
A) center: (0, 0) vertices: (0, -5), (0, 5) 
B) center: (0, 0) vertices: (-3, 0), (3, 0) 
C) center: (5, 3) vertices: (-5, -3), (5, 3) 
D) center: (0, 0) vertices: (-5, 0), (5, 0) 
E) center: (5, 0) vertices: (0, -3), (0, 3)

Question 12

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. 
Directrix: y = 2

Accepted Answer

A)  $x ^ { 2 } = - 8 y$ 
B)  $x ^ { 2 } = 8 y$ 
C)  $y ^ { 2 } = - 8 x$ 
D)  $y ^ { 2 } = 8 x$ 
E)  $x ^ { 2 } = - \frac { y } { 8 }$ 
A)  $x ^ { 2 } = - 8 y$ 
B)  $x ^ { 2 } = 8 y$ 
C)  $y ^ { 2 } = - 8 x$ 
D)  $y ^ { 2 } = 8 x$ 
E)  $x ^ { 2 } = - \frac { y } { 8 }$

Question 13

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.  $\begin{array} { l } 
0.04 x + 0.02 y = - 0.06 \
0.05 x - 0.04 y = 0.03
\end{array}$

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)  $\theta \approx 1.1071 \text { radians } \approx 61.4 ^ { \circ }$ 
E)  $\theta \approx 1.1071 \text { radians } \approx 63.4 ^ { \circ }$ 
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)  $\theta \approx 1.1071 \text { radians } \approx 61.4 ^ { \circ }$ 
E)  $\theta \approx 1.1071 \text { radians } \approx 63.4 ^ { \circ }$

Question 14

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Accepted Answer

A)  $x ^ { 2 } = \frac { 1 } { 9 } y$ focus: $\left( 0 , \frac { 1 } { 36 } \right)$ 
B)  $x ^ { 2 } = - \frac { 1 } { 36 } y$ focus: $\left( 0 , - \frac { 1 } { 36 } \right)$ 
C)  $x ^ { 2 } = \frac { 1 } { 9 } y$ focus: $\left( 0 , - \frac { 1 } { 9 } \right)$ 
D)  $x ^ { 2 } = 9 y$ focus: $\left( 0 , - \frac { 1 } { 9 } \right)$ 
E)  $x ^ { 2 } = - 9 y$ focus: (0, 4) 
A)  $x ^ { 2 } = \frac { 1 } { 9 } y$ focus: $\left( 0 , \frac { 1 } { 36 } \right)$ 
B)  $x ^ { 2 } = - \frac { 1 } { 36 } y$ focus: $\left( 0 , - \frac { 1 } { 36 } \right)$ 
C)  $x ^ { 2 } = \frac { 1 } { 9 } y$ focus: $\left( 0 , - \frac { 1 } { 9 } \right)$ 
D)  $x ^ { 2 } = 9 y$ focus: $\left( 0 , - \frac { 1 } { 9 } \right)$ 
E)  $x ^ { 2 } = - 9 y$ focus: (0, 4)

Question 15

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. 
Vertices: $( 0 , \pm 5 )$ ; foci: $( 0 , \pm 9 )$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 56 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 56 } = 1$ 
C)  $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 56 } = 1$ 
D)  $\frac { y ^ { 2 } } { 56 } - \frac { x ^ { 2 } } { 25 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 56 } = 1$ 
A)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 56 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 56 } = 1$ 
C)  $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 56 } = 1$ 
D)  $\frac { y ^ { 2 } } { 56 } - \frac { x ^ { 2 } } { 25 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 56 } = 1$

Question 16

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

Accepted Answer

A) Symmetric with respect to the polar axis $| r | = 1$ when $\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi$ $r = 0$ when $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$    
B) Symmetric with respect to the polar axis $| r | = 1$ when $\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi$ $r = 0$ when $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$    
C) Symmetric with respect to the polar axis $| r | = 1$ when $\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi$ 
$r = 0$ when $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$    
D) Symmetric with respect to the polar axis $| r | = 1$ when $\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi$ 
$r = 0$ when $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$   
E) Symmetric with respect to the polar axis $| r | = 1$ when $\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi$ 
$r = 0$ when $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$    
A) Symmetric with respect to the polar axis $| r | = 1$ when $\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi$ $r = 0$ when $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$    
B) Symmetric with respect to the polar axis $| r | = 1$ when $\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi$ $r = 0$ when $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$    
C) Symmetric with respect to the polar axis $| r | = 1$ when $\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi$ 
$r = 0$ when $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$    
D) Symmetric with respect to the polar axis $| r | = 1$ when $\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi$ 
$r = 0$ when $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$   
E) Symmetric with respect to the polar axis $| r | = 1$ when $\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi$ 
$r = 0$ when $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$

Question 17

Select the graph of the following equation.  $y = x \pm 5$

Accepted Answer

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

Question 18

Identify the conic by writing the equation in standard form. $10 y ^ { 2 } - 20 x ^ { 2 } + 80 y + 360 x - 1485 = 0$

Accepted Answer

A)  $\frac { ( y - 4 ) ^ { 2 } } { \frac { 5 } { 2 } } - \frac { ( x - 9 ) ^ { 2 } } { \frac { 5 } { 4 } } = 1$ ; hyperbola 
B)  $\frac { ( y + 4 ) ^ { 2 } } { \frac { 5 } { 2 } } - \frac { ( x - 9 ) ^ { 2 } } { \frac { 5 } { 4 } } = 1$ ; hyperbola 
C)  $\frac { ( y + 4 ) ^ { 2 } } { \frac { 97 } { 2 } } - \frac { ( x - 9 ) ^ { 2 } } { \frac { 97 } { 4 } } = 1$ ; hyperbola 
D)  $\frac { ( y + 4 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 9 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ; ellipse 
E)  $\frac { ( y - 4 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 9 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ; ellipse 
A)  $\frac { ( y - 4 ) ^ { 2 } } { \frac { 5 } { 2 } } - \frac { ( x - 9 ) ^ { 2 } } { \frac { 5 } { 4 } } = 1$ ; hyperbola 
B)  $\frac { ( y + 4 ) ^ { 2 } } { \frac { 5 } { 2 } } - \frac { ( x - 9 ) ^ { 2 } } { \frac { 5 } { 4 } } = 1$ ; hyperbola 
C)  $\frac { ( y + 4 ) ^ { 2 } } { \frac { 97 } { 2 } } - \frac { ( x - 9 ) ^ { 2 } } { \frac { 97 } { 4 } } = 1$ ; hyperbola 
D)  $\frac { ( y + 4 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 9 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ; ellipse 
E)  $\frac { ( y - 4 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 9 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ; ellipse

Question 19

Find a set of parametric equations for the rectangular equation.  $t = 2 - x$ $y = \frac { 1 } { 3 x }$

Accepted Answer

A)  $x = - 2 - t , y = \frac { 1 } { ( 6 - 6 t ) }$ 
B)  $x = - 2 - t , y = \frac { 1 } { ( 6 - 3 t ) }$ 
C)  $x = 2 - t , y = \frac { 1 } { ( 3 - 3 t ) }$ 
D)  $x = - 2 + t , y = \frac { 1 } { ( 6 - 3 t ) }$ 
E)  $x = 2 - t , y = \frac { 1 } { ( 6 - 3 t ) }$ 
A)  $x = - 2 - t , y = \frac { 1 } { ( 6 - 6 t ) }$ 
B)  $x = - 2 - t , y = \frac { 1 } { ( 6 - 3 t ) }$ 
C)  $x = 2 - t , y = \frac { 1 } { ( 3 - 3 t ) }$ 
D)  $x = - 2 + t , y = \frac { 1 } { ( 6 - 3 t ) }$ 
E)  $x = 2 - t , y = \frac { 1 } { ( 6 - 3 t ) }$

Question 20

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -9

Accepted Answer

A) x2 = -9y 
B) y2 = 36x 
C) x2 = -36y 
D) x2 = 36y 
E) y2 = -9x 
A) x2 = -9y 
B) y2 = 36x 
C) x2 = -36y 
D) x2 = 36y 
E) y2 = -9x

Select the graph of degenerate conic. $x ^ { 2 } + y ^ { 2 } - 2 x + 16 y + 65 = 0$

Select the graph of $r = 3 \cos \theta$ over the interval.Describe the part of the graph obtained in this case. $- \frac { \pi } { 2 } \leq \theta \leq \frac { \pi } { 2 }$

Find the center and vertices of the ellipse. $x ^ { 2 } + 16 y ^ { 2 } - 10 x - 32 y + 25 = 0$

Select the graph for following equation. $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

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. 0.04x+0.02y=0.06 0.07x-0.06y=0.05

Find the vertex, focus, and directrix of the parabola. $( x - 1 ) ^ { 2 } + 16 ( y + 6 ) = 0$

Find the center, vertices and foci of the hyperbola. $\frac { y ^ { 2 } } { 1 } - \frac { x ^ { 2 } } { 36 } = 1$

A roof has a rise of 9 feet for every horizontal change of 11 feet (see figure).Find the inclination of the roof.Round your answers to one decimal place. $a = 9 , b = 11$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $y ^ { 2 } - 4 x ^ { 2 } + 4 x - 8 y - 24 = 0$

Write the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (5, 0).

Find the center and vertices which located on the major axis of the ellipse. $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: y = 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. 0.04x+0.02y=-0.06 0.05x-0.04y=0.03

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: $( 0 , \pm 5 )$ ; foci: $( 0 , \pm 9 )$

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

Select the graph of the following equation. $y = x \pm 5$

Identify the conic by writing the equation in standard form. $10 y ^ { 2 } - 20 x ^ { 2 } + 80 y + 360 x - 1485 = 0$

Find a set of parametric equations for the rectangular equation. $t = 2 - x$ $y = \frac { 1 } { 3 x }$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -9

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 graph of degenerate conic. x2+y2−2x+16y+65=0x ^ { 2 } + y ^ { 2 } - 2 x + 16 y + 65 = 0x2+y2−2x+16y+65=0

Select the graph of r=3cos⁡θr = 3 \cos \thetar=3cosθ over the interval.Describe the part of the graph obtained in this case. −π2≤θ≤π2- \frac { \pi } { 2 } \leq \theta \leq \frac { \pi } { 2 }−2π​≤θ≤2π​

Find the center and vertices of the ellipse. x2+16y2−10x−32y+25=0x ^ { 2 } + 16 y ^ { 2 } - 10 x - 32 y + 25 = 0x2+16y2−10x−32y+25=0

Select the graph for following equation. x29+y216=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 19x2​+16y2​=1

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. 0.04x+0.02y=0.06 0.07x-0.06y=0.05

Find the vertex, focus, and directrix of the parabola. (x−1)2+16(y+6)=0( x - 1 ) ^ { 2 } + 16 ( y + 6 ) = 0(x−1)2+16(y+6)=0

Find the center, vertices and foci of the hyperbola. y21−x236=1\frac { y ^ { 2 } } { 1 } - \frac { x ^ { 2 } } { 36 } = 11y2​−36x2​=1

A roof has a rise of 9 feet for every horizontal change of 11 feet (see figure).Find the inclination of the roof.Round your answers to one decimal place. a=9,b=11a = 9 , b = 11a=9,b=11

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. y2−4x2+4x−8y−24=0y ^ { 2 } - 4 x ^ { 2 } + 4 x - 8 y - 24 = 0y2−4x2+4x−8y−24=0

Write the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (5, 0).

Find the center and vertices which located on the major axis of the ellipse. x225+y29=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 125x2​+9y2​=1

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: y = 2

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. 0.04x+0.02y=-0.06 0.05x-0.04y=0.03

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±5)( 0 , \pm 5 )(0,±5) ; foci: (0,±9)( 0 , \pm 9 )(0,±9)

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=cos⁡3θr = \cos 3 \thetar=cos3θ

Select the graph of the following equation. y=x±5y = x \pm 5y=x±5

Identify the conic by writing the equation in standard form. 10y2−20x2+80y+360x−1485=010 y ^ { 2 } - 20 x ^ { 2 } + 80 y + 360 x - 1485 = 010y2−20x2+80y+360x−1485=0

Find a set of parametric equations for the rectangular equation. t=2−xt = 2 - xt=2−x y=13xy = \frac { 1 } { 3 x }y=3x1​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -9

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 the graph of degenerate conic. $x ^ { 2 } + y ^ { 2 } - 2 x + 16 y + 65 = 0$

Select the graph of $r = 3 \cos \theta$ over the interval.Describe the part of the graph obtained in this case. $- \frac { \pi } { 2 } \leq \theta \leq \frac { \pi } { 2 }$

Find the center and vertices of the ellipse. $x ^ { 2 } + 16 y ^ { 2 } - 10 x - 32 y + 25 = 0$

Select the graph for following equation. $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

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. 0.04x+0.02y=0.06 0.07x-0.06y=0.05

Find the vertex, focus, and directrix of the parabola. $( x - 1 ) ^ { 2 } + 16 ( y + 6 ) = 0$

Find the center, vertices and foci of the hyperbola. $\frac { y ^ { 2 } } { 1 } - \frac { x ^ { 2 } } { 36 } = 1$

A roof has a rise of 9 feet for every horizontal change of 11 feet (see figure).Find the inclination of the roof.Round your answers to one decimal place. $a = 9 , b = 11$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $y ^ { 2 } - 4 x ^ { 2 } + 4 x - 8 y - 24 = 0$

Find the center and vertices which located on the major axis of the ellipse. $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$

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. 0.04x+0.02y=-0.06 0.05x-0.04y=0.03

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: $( 0 , \pm 5 )$ ; foci: $( 0 , \pm 9 )$

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

Select the graph of the following equation. $y = x \pm 5$

Identify the conic by writing the equation in standard form. $10 y ^ { 2 } - 20 x ^ { 2 } + 80 y + 360 x - 1485 = 0$

Find a set of parametric equations for the rectangular equation. $t = 2 - x$ $y = \frac { 1 } { 3 x }$