Question 1

Match the equation with its graph. $x ^ { 2 } + 9 y ^ { 2 } = 9$

Accepted Answer

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

Question 2

The Roman Coliseum is an elliptical amphitheater measuring approximately 188 meters long and 156 meters wide.Find an equation to model the coliseum that is of the form  $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ .

Accepted Answer

A)  $\frac { x ^ { 2 } } { 6084 } - \frac { y ^ { 2 } } { 8836 } = 1$ 
B)  $\frac { x ^ { 2 } } { 8836 } + \frac { y ^ { 2 } } { 6084 } = 1$ 
C)  $\frac { x ^ { 2 } } { 8836 } + \frac { y ^ { 2 } } { 6084 } = 0$ 
D)  $\frac { x ^ { 2 } } { 188 ^ { 2 } } + \frac { y ^ { 2 } } { 156 ^ { 2 } } = 1$ 
E)  $\frac { x ^ { 2 } } { 6084 } + \frac { y ^ { 2 } } { 8836 } = 0$ 
A)  $\frac { x ^ { 2 } } { 6084 } - \frac { y ^ { 2 } } { 8836 } = 1$ 
B)  $\frac { x ^ { 2 } } { 8836 } + \frac { y ^ { 2 } } { 6084 } = 1$ 
C)  $\frac { x ^ { 2 } } { 8836 } + \frac { y ^ { 2 } } { 6084 } = 0$ 
D)  $\frac { x ^ { 2 } } { 188 ^ { 2 } } + \frac { y ^ { 2 } } { 156 ^ { 2 } } = 1$ 
E)  $\frac { x ^ { 2 } } { 6084 } + \frac { y ^ { 2 } } { 8836 } = 0$

Question 3

Select the correct graph of the polar equation.Find an interval for $\theta$ for which the graph is traced only once.  $r = 5 + 4 \cos \theta$

Accepted Answer

A)    $0 \leq \theta < 2 \pi$ 
B)    $0 \leq \theta < 2 \pi$ 
C)    $0 \leq \theta < 2 \pi$ 
D)    $0 \leq \theta < 2 \pi$ 
E)   $0 \leq \theta < 2 \pi$ 
A)    $0 \leq \theta < 2 \pi$ 
B)    $0 \leq \theta < 2 \pi$ 
C)    $0 \leq \theta < 2 \pi$ 
D)    $0 \leq \theta < 2 \pi$ 
E)   $0 \leq \theta < 2 \pi$

Question 4

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.  $8 x ^ { 2 } - 4 y ^ { 2 } - 16 x - 3 = 0$

Accepted Answer

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

Question 5

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $5 x ^ { 2 } - 10 x y + 12 y ^ { 2 } + ( 5 \sqrt { 11 } - 10 ) x - ( 7 \sqrt { 11 } + 11 ) y = 93$

Accepted Answer

A)  $\theta = 78.87 ^ { \circ }$ 
B)  $\theta = 77.87 ^ { \circ }$ 
C)  $\theta = 79.87 ^ { \circ }$ 
D)  $\theta = 80.87 ^ { \circ }$ 
E)  $\theta = 81.87 ^ { \circ }$ 
A)  $\theta = 78.87 ^ { \circ }$ 
B)  $\theta = 77.87 ^ { \circ }$ 
C)  $\theta = 79.87 ^ { \circ }$ 
D)  $\theta = 80.87 ^ { \circ }$ 
E)  $\theta = 81.87 ^ { \circ }$

Question 6

Select the polar equation of the conic for e = 0.75 and identify the conic for the following equation.  $r = \frac { 2 e } { 1 - e \cos \theta }$

Accepted Answer

A)  $r = \frac { 1.5 } { 1 - 0.75 \cos \theta } \Rightarrow \text { ellipse }$ 
B)  $r = \frac { 1.5 } { 1 - 1.75 \cos \theta } \Rightarrow \text { parabola }$ 
C)  $r = \frac { 0.75 } { 1 + 0.75 \cos \theta } \Rightarrow \text { parabola }$ 
D)  $r = \frac { 1.5 } { 1 + \cos \theta } \Rightarrow \text { ellipse }$ 
E)  $r = \frac { 1.75 } { 1 + \cos \theta } \Rightarrow \text { parabola }$ 
A)  $r = \frac { 1.5 } { 1 - 0.75 \cos \theta } \Rightarrow \text { ellipse }$ 
B)  $r = \frac { 1.5 } { 1 - 1.75 \cos \theta } \Rightarrow \text { parabola }$ 
C)  $r = \frac { 0.75 } { 1 + 0.75 \cos \theta } \Rightarrow \text { parabola }$ 
D)  $r = \frac { 1.5 } { 1 + \cos \theta } \Rightarrow \text { ellipse }$ 
E)  $r = \frac { 1.75 } { 1 + \cos \theta } \Rightarrow \text { parabola }$

Question 7

Using following result find a set of parametric equation of conic. 
Hyperbola: $x = h + a \sec \theta , y = k + b \tan \theta$ 
Hyperbola: vertices: $( \pm 4,0 )$ ; foci: $( \pm 5,0 )$

Accepted Answer

A)  $x = 5 + 4 \sec \theta , y = 5 + 3 \tan \theta$ 
B)  $x = 4 \sec \theta , y = 3 \tan \theta$ 
C)  $x = 5 - 4 \sec \theta , y = 3 \tan \theta$ 
D)  $x = 3 \sec \theta , y = 4 \tan \theta$ 
E)  $x = 5 \sec \theta , y = 4 \tan \theta$ 
A)  $x = 5 + 4 \sec \theta , y = 5 + 3 \tan \theta$ 
B)  $x = 4 \sec \theta , y = 3 \tan \theta$ 
C)  $x = 5 - 4 \sec \theta , y = 3 \tan \theta$ 
D)  $x = 3 \sec \theta , y = 4 \tan \theta$ 
E)  $x = 5 \sec \theta , y = 4 \tan \theta$

Question 8

Select correct graph to graph rotated conic.  $r = \frac { 2 } { - 1 + 2 \cos ( \theta + 2 \pi / 3 ) }$

Accepted Answer

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

Question 9

Find the vertex and focus of the parabola for the given equation and select its graph. $y ^ { 2 } = - 4 x$

Accepted Answer

A) Vertex: (0,0)Focus: (1,0)   
B) Vertex: (0,0)Focus: (1,0)   
C) Vertex: (0,0)Focus: (-1,0)   
D) Vertex: (0,0)Focus: ( - 1,0)   
E) Vertex: (0,0)Focus: (0,1)   
A) Vertex: (0,0)Focus: (1,0)   
B) Vertex: (0,0)Focus: (1,0)   
C) Vertex: (0,0)Focus: (-1,0)   
D) Vertex: (0,0)Focus: ( - 1,0)   
E) Vertex: (0,0)Focus: (0,1)

Question 10

Find the standard form of the equation of the ellipse with the following characteristics. 
Foci: $( \pm 3,0 )$ , major axis of length: 16

Accepted Answer

A)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 55 } = 1$ 
B)  $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 247 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 9 } = 1$ 
E)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 64 } = 1$ 
A)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 55 } = 1$ 
B)  $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 247 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 9 } = 1$ 
E)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 11

Convert the polar equation to rectangular form. $r = 3 \cos \theta$

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } + 3 y = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 3 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 3 y = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 3 x = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - 3 x = 0$ 
A)  $x ^ { 2 } + y ^ { 2 } + 3 y = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 3 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 3 y = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 3 x = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - 3 x = 0$

Question 12

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.  $\begin{array} { l } 
x - y = 10 \
3 x - 2 y = 1
\end{array}$

Accepted Answer

A)  $\Theta \approx 0.0907 \text { radians } \approx 6.2 ^ { \circ }$ 
B)  $\Theta \approx 0.0907 \text { radians } \approx 4.2 ^ { \circ }$ 
C)  $\Theta \approx 0.0907 \text { radians } \approx 5.2 ^ { \circ }$ 
D)  $\Theta \approx 0.0907 \text { radians } \approx 7.2 ^ { \circ }$ 
E)  $\Theta \approx 0.0907 \text { radians } \approx 3.2 ^ { \circ }$ 
A)  $\Theta \approx 0.0907 \text { radians } \approx 6.2 ^ { \circ }$ 
B)  $\Theta \approx 0.0907 \text { radians } \approx 4.2 ^ { \circ }$ 
C)  $\Theta \approx 0.0907 \text { radians } \approx 5.2 ^ { \circ }$ 
D)  $\Theta \approx 0.0907 \text { radians } \approx 7.2 ^ { \circ }$ 
E)  $\Theta \approx 0.0907 \text { radians } \approx 3.2 ^ { \circ }$

Question 13

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 4,0 )$ asymptotes: $y = \pm 5 x$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { \frac { 16 } { 26 } } - \frac { x ^ { 2 } } { \frac { 400 } { 26 } } = 1$ 
D)  $\frac { x ^ { 2 } } { \frac { 16 } { 26 } } - \frac { y ^ { 2 } } { \frac { 400 } { 26 } } = 1$ 
E)  $\frac { x ^ { 2 } } { \frac { 400 } { 26 } } - \frac { y ^ { 2 } } { \frac { 16 } { 26 } } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { \frac { 16 } { 26 } } - \frac { x ^ { 2 } } { \frac { 400 } { 26 } } = 1$ 
D)  $\frac { x ^ { 2 } } { \frac { 16 } { 26 } } - \frac { y ^ { 2 } } { \frac { 400 } { 26 } } = 1$ 
E)  $\frac { x ^ { 2 } } { \frac { 400 } { 26 } } - \frac { y ^ { 2 } } { \frac { 16 } { 26 } } = 1$

Question 14

Identify the conic and select its correct graph.  $r = \frac { 2 } { 2 - 4 \cos \theta }$

Accepted Answer

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

Question 15

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. 
Directrix: x = -4

Accepted Answer

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

Question 16

Give the coordinates of the circle's center and it radius.
  $( x - 7 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 16$  
Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

Accepted Answer

The answer of Give the coordinates of the circle's center...

Question 17

The revenue R (in dollars) generated by the sale of x units of a digital camera is given by $( x - 145 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 29,435 )$ .Approximate the number of sales that will maximize revenue.

Accepted Answer

A) Maximum revenue occurs at $x = 4,205$ units. 
B) Maximum revenue occurs at $x = 406$ units. 
C) Maximum revenue occurs at $x = 145$ units. 
D) Maximum revenue occurs at $x = 29,435$ units. 
E) Maximum revenue occurs at $x = 21,025$ units. 
A) Maximum revenue occurs at $x = 4,205$ units. 
B) Maximum revenue occurs at $x = 406$ units. 
C) Maximum revenue occurs at $x = 145$ units. 
D) Maximum revenue occurs at $x = 29,435$ units. 
E) Maximum revenue occurs at $x = 21,025$ units.

Question 18

A projectile is launched at a height of h feet above the ground at an angle of $\theta$ with the horizontal.The initial velocity is $v _ { 0 }$ feet per second, and the path of the projectile is modeled by the parametric equations $x = \left( v _ { 0 } \cos \theta \right) t \text { and } y = h + \left( v _ { 0 } \sin \theta \right) t - 16 t ^ { 2 }$ . Select the correct graph of the path of a projectile launched from ground level at the value of $\theta$ and $v _ { 0 }$ .
 $\theta = 10 ^ { \circ } , v _ { 0 } = 70$ feet per second

Accepted Answer

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

Question 19

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.  $\theta = 90 ^ { \circ }$ , $( 0,3 )$

Accepted Answer

A)  $( 0,4 )$ 
B)  $( - 3,3 )$ 
C)  $( - 3,0 )$ 
D)  $( 3,0 )$ 
E)  $( 0,3 )$ 
A)  $( 0,4 )$ 
B)  $( - 3,3 )$ 
C)  $( - 3,0 )$ 
D)  $( 3,0 )$ 
E)  $( 0,3 )$

Question 20

Select the curve represented by the parametric equations.  $x = 1 + \cos \theta$ $y = 1 + 2 \sin \theta$

Accepted Answer

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

Match the equation with its graph. $x ^ { 2 } + 9 y ^ { 2 } = 9$

The Roman Coliseum is an elliptical amphitheater measuring approximately 188 meters long and 156 meters wide.Find an equation to model the coliseum that is of the form $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ .

Select the correct graph of the polar equation.Find an interval for $\theta$ for which the graph is traced only once. $r = 5 + 4 \cos \theta$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $8 x ^ { 2 } - 4 y ^ { 2 } - 16 x - 3 = 0$

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $5 x ^ { 2 } - 10 x y + 12 y ^ { 2 } + ( 5 \sqrt { 11 } - 10 ) x - ( 7 \sqrt { 11 } + 11 ) y = 93$

Select the polar equation of the conic for e = 0.75 and identify the conic for the following equation. $r = \frac { 2 e } { 1 - e \cos \theta }$

Using following result find a set of parametric equation of conic. Hyperbola: $x = h + a \sec \theta , y = k + b \tan \theta$ Hyperbola: vertices: $( \pm 4,0 )$ ; foci: $( \pm 5,0 )$

Select correct graph to graph rotated conic. $r = \frac { 2 } { - 1 + 2 \cos ( \theta + 2 \pi / 3 ) }$

Find the vertex and focus of the parabola for the given equation and select its graph. $y ^ { 2 } = - 4 x$

Find the standard form of the equation of the ellipse with the following characteristics. Foci: $( \pm 3,0 )$ , major axis of length: 16

Convert the polar equation to rectangular form. $r = 3 \cos \theta$

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. x-y=10 3x-2y=1

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 4,0 )$ asymptotes: $y = \pm 5 x$

Identify the conic and select its correct graph. $r = \frac { 2 } { 2 - 4 \cos \theta }$

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: x = -4

Give the coordinates of the circle's center and it radius. $( x - 7 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 16$ Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

The revenue R (in dollars) generated by the sale of x units of a digital camera is given by $( x - 145 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 29,435 )$ .Approximate the number of sales that will maximize revenue.

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. $\theta = 90 ^ { \circ }$ , $( 0,3 )$

Select the curve represented by the parametric equations. $x = 1 + \cos \theta$ $y = 1 + 2 \sin \theta$

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

Sequences Series and Probability

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 10: Topics In Analytic Geometry

Match the equation with its graph. x2+9y2=9x ^ { 2 } + 9 y ^ { 2 } = 9x2+9y2=9

The Roman Coliseum is an elliptical amphitheater measuring approximately 188 meters long and 156 meters wide.Find an equation to model the coliseum that is of the form x2a2+y2b2=1\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1a2x2​+b2y2​=1 .

Select the correct graph of the polar equation.Find an interval for θ\thetaθ for which the graph is traced only once. r=5+4cos⁡θr = 5 + 4 \cos \thetar=5+4cosθ

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 8x2−4y2−16x−3=08 x ^ { 2 } - 4 y ^ { 2 } - 16 x - 3 = 08x2−4y2−16x−3=0

Determine the angle θ\thetaθ through which the axes are rotated.Round your answer to two decimal places. 5x2−10xy+12y2+(511−10)x−(711+11)y=935 x ^ { 2 } - 10 x y + 12 y ^ { 2 } + ( 5 \sqrt { 11 } - 10 ) x - ( 7 \sqrt { 11 } + 11 ) y = 935x2−10xy+12y2+(511​−10)x−(711​+11)y=93

Select the polar equation of the conic for e = 0.75 and identify the conic for the following equation. r=2e1−ecos⁡θr = \frac { 2 e } { 1 - e \cos \theta }r=1−ecosθ2e​

Using following result find a set of parametric equation of conic. Hyperbola: x=h+asec⁡θ,y=k+btan⁡θx = h + a \sec \theta , y = k + b \tan \thetax=h+asecθ,y=k+btanθ Hyperbola: vertices: (±4,0)( \pm 4,0 )(±4,0) ; foci: (±5,0)( \pm 5,0 )(±5,0)

Select correct graph to graph rotated conic. r=2−1+2cos⁡(θ+2π/3)r = \frac { 2 } { - 1 + 2 \cos ( \theta + 2 \pi / 3 ) }r=−1+2cos(θ+2π/3)2​

Find the vertex and focus of the parabola for the given equation and select its graph. y2=−4xy ^ { 2 } = - 4 xy2=−4x

Find the standard form of the equation of the ellipse with the following characteristics. Foci: (±3,0)( \pm 3,0 )(±3,0) , major axis of length: 16

Convert the polar equation to rectangular form. r=3cos⁡θr = 3 \cos \thetar=3cosθ

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=10 3x-2y=1

Find the standard form of the equation of the hyperbola with the given characteristics. foci: (±4,0)( \pm 4,0 )(±4,0) asymptotes: y=±5xy = \pm 5 xy=±5x

Identify the conic and select its correct graph. r=22−4cos⁡θr = \frac { 2 } { 2 - 4 \cos \theta }r=2−4cosθ2​

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: x = -4

Give the coordinates of the circle's center and it radius. (x−7)2+(y+8)2=16( x - 7 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 16(x−7)2+(y+8)2=16 Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

The revenue R (in dollars) generated by the sale of x units of a digital camera is given by (x−145)2=−57(R−29,435)( x - 145 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 29,435 )(x−145)2=−75​(R−29,435) .Approximate the number of sales that will maximize revenue.

Select the curve represented by the parametric equations. x=1+cos⁡θx = 1 + \cos \thetax=1+cosθ y=1+2sin⁡θy = 1 + 2 \sin \thetay=1+2sinθ

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

Match the equation with its graph. $x ^ { 2 } + 9 y ^ { 2 } = 9$

The Roman Coliseum is an elliptical amphitheater measuring approximately 188 meters long and 156 meters wide.Find an equation to model the coliseum that is of the form $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ .

Select the correct graph of the polar equation.Find an interval for $\theta$ for which the graph is traced only once. $r = 5 + 4 \cos \theta$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $8 x ^ { 2 } - 4 y ^ { 2 } - 16 x - 3 = 0$

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $5 x ^ { 2 } - 10 x y + 12 y ^ { 2 } + ( 5 \sqrt { 11 } - 10 ) x - ( 7 \sqrt { 11 } + 11 ) y = 93$

Select the polar equation of the conic for e = 0.75 and identify the conic for the following equation. $r = \frac { 2 e } { 1 - e \cos \theta }$

Using following result find a set of parametric equation of conic. Hyperbola: $x = h + a \sec \theta , y = k + b \tan \theta$ Hyperbola: vertices: $( \pm 4,0 )$ ; foci: $( \pm 5,0 )$

Select correct graph to graph rotated conic. $r = \frac { 2 } { - 1 + 2 \cos ( \theta + 2 \pi / 3 ) }$

Find the vertex and focus of the parabola for the given equation and select its graph. $y ^ { 2 } = - 4 x$

Find the standard form of the equation of the ellipse with the following characteristics. Foci: $( \pm 3,0 )$ , major axis of length: 16

Convert the polar equation to rectangular form. $r = 3 \cos \theta$

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. x-y=10 3x-2y=1

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 4,0 )$ asymptotes: $y = \pm 5 x$

Identify the conic and select its correct graph. $r = \frac { 2 } { 2 - 4 \cos \theta }$

Give the coordinates of the circle's center and it radius. $( x - 7 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 16$ Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

The revenue R (in dollars) generated by the sale of x units of a digital camera is given by $( x - 145 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 29,435 )$ .Approximate the number of sales that will maximize revenue.

Select the curve represented by the parametric equations. $x = 1 + \cos \theta$ $y = 1 + 2 \sin \theta$