Question 1

Find the vertex and focus of the parabola from the given equation and select its graph.  $y = \frac { 1 } { 6 } x ^ { 2 }$

Accepted Answer

A) Vertex: (0,0)Focus: (0,-1.5)   
B) Vertex: (0,0)Focus: (-1.5,0)   
C) Vertex: (0,0)Focus: (0,1.5)   
D) Vertex: (0,0)Focus: (0,1.5)   
E) Vertex: (0,0)Focus: (0,-1.5)   
A) Vertex: (0,0)Focus: (0,-1.5)   
B) Vertex: (0,0)Focus: (-1.5,0)   
C) Vertex: (0,0)Focus: (0,1.5)   
D) Vertex: (0,0)Focus: (0,1.5)   
E) Vertex: (0,0)Focus: (0,-1.5)

Question 2

Find the equation of the hyperbola with vertices (2, 0), (-2, 0) and focus (4, 0).

Accepted Answer

A)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 12 } = 1$ 
B)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 12 } = 1$ 
C)  $\frac { x ^ { 2 } } { 12 } - \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 12 } = 1$ 
E) none of these 
A)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 12 } = 1$ 
B)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 12 } = 1$ 
C)  $\frac { x ^ { 2 } } { 12 } - \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 12 } = 1$ 
E) none of these

Question 3

Find a polar equation of the conic with its focus at the pole. 
Conics $\quad$$\quad$Eccentricity$\quad$$\quad$ Directrix
Ellipse $\quad\quad\quad e = 2\quad\quad\quad x = 1$

Accepted Answer

A)  $r = \frac { 2 } { 1 + \cos \theta }$ 
B)  $r = \frac { 2 } { 1 + 2 \cos \theta }$ 
C)  $r = \frac { - 2 } { 1 - \cos \theta }$ 
D)  $r = \frac { 2 } { 1 - \sin \theta }$ 
E)  $r = \frac { 2 } { 1 + 2 \sin \theta }$ 
A)  $r = \frac { 2 } { 1 + \cos \theta }$ 
B)  $r = \frac { 2 } { 1 + 2 \cos \theta }$ 
C)  $r = \frac { - 2 } { 1 - \cos \theta }$ 
D)  $r = \frac { 2 } { 1 - \sin \theta }$ 
E)  $r = \frac { 2 } { 1 + 2 \sin \theta }$

Question 4

Find the center and vertices of the ellipse.  $x ^ { 2 } + 4 y ^ { 2 } - 6 x + 8 y + 9 = 0$

Accepted Answer

A) center: (-1, 3), vertices: (-3, 3), (1, 3) 
B) center: (-3, 1), vertices: (-4, 1), (-2, 1) 
C) center: (3, -1), vertices: (2, -1), (4, -1) 
D) center: (3, -1), vertices: (1, -1), (5, -1) 
E) center: (-3, 1), vertices: (-5, 1), (-1, 1) 
A) center: (-1, 3), vertices: (-3, 3), (1, 3) 
B) center: (-3, 1), vertices: (-4, 1), (-2, 1) 
C) center: (3, -1), vertices: (2, -1), (4, -1) 
D) center: (3, -1), vertices: (1, -1), (5, -1) 
E) center: (-3, 1), vertices: (-5, 1), (-1, 1)

Question 5

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

Accepted Answer

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

Question 6

Graph the following equation.  $x ^ { 2 } - 6 x + y ^ { 2 } = 7$

Accepted Answer

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

Question 7

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = 2 ( 1 - \sin \theta )$

Accepted Answer

A) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
B) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
C) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
D) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
E) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
A) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
B) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
C) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
D) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
E) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$

Question 8

Find a polar equation of the conic with its focus at the pole. 
Conics $\quad$$\quad$Eccentricity$\quad$$\quad$ Directrix
Ellipse $\quad\quad\quad e = \frac { 1 } { 2 } \quad\quad\quad y = 3$

Accepted Answer

A)  $r = \frac { 3 } { 2 + \sin \theta }$ 
B)  $r = \frac { 3 } { 2 - 4 \sin \theta }$ 
C)  $r = \frac { 4 } { 2 - \sin \theta }$ 
D)  $r = \frac { - 3 } { 2 - \sin \theta }$ 
E)  $r = \frac { 3 } { 2 - \sin \theta }$ 
A)  $r = \frac { 3 } { 2 + \sin \theta }$ 
B)  $r = \frac { 3 } { 2 - 4 \sin \theta }$ 
C)  $r = \frac { 4 } { 2 - \sin \theta }$ 
D)  $r = \frac { - 3 } { 2 - \sin \theta }$ 
E)  $r = \frac { 3 } { 2 - \sin \theta }$

Question 9

Using following result find a set of parametric equation of conic. 
Hyperbola: $x = h + a \sec \theta , y = k + b \tan \theta$ 
Hyperbola: vertices: $( \pm 15,0 )$ ; foci: $( \pm 17,0 )$

Accepted Answer

A)  $x = 8 \sec \theta , y = 15 \tan \theta$ 
B)  $x = 17 - 15 \sec \theta , y = 17 + 8 \tan \theta$ 
C)  $x = 15 \sec \theta , y = 8 \tan \theta$ 
D)  $x = - 8 + 15 \sec \theta , y = 17 - 8 \tan \theta$ 
E)  $x = 17 \sec \theta , y = 17 \tan \theta$ 
A)  $x = 8 \sec \theta , y = 15 \tan \theta$ 
B)  $x = 17 - 15 \sec \theta , y = 17 + 8 \tan \theta$ 
C)  $x = 15 \sec \theta , y = 8 \tan \theta$ 
D)  $x = - 8 + 15 \sec \theta , y = 17 - 8 \tan \theta$ 
E)  $x = 17 \sec \theta , y = 17 \tan \theta$

Question 10

Convert the polar equation to rectangular form. $r = - 5 \cos \theta$

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } - 5 x = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 5 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } + 5 x = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } - 5 y = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } + 5 y = 0$ 
A)  $x ^ { 2 } + y ^ { 2 } - 5 x = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 5 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } + 5 x = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } - 5 y = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } + 5 y = 0$

Question 11

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

Accepted Answer

A)  $x ^ { 2 } = - 4 y$ , focus: $\left( 0 , - \frac { 1 } { 4 } \right)$ 
B)  $x ^ { 2 } = - \frac { 1 } { 16 } y$ , focus: $\left( 0 , - \frac { 1 } { 16 } \right)$ 
C)  $x ^ { 2 } = - \frac { 1 } { 4 } y$ , focus: $\left( 0 , - \frac { 1 } { 16 } \right)$ 
D)  $x ^ { 2 } = - 4 y$ , focus: (0,-4) 
E)  $x ^ { 2 } = - \frac { 1 } { 4 } y$ , focus: $\left( 0 , - \frac { 1 } { 4 } \right)$ 
A)  $x ^ { 2 } = - 4 y$ , focus: $\left( 0 , - \frac { 1 } { 4 } \right)$ 
B)  $x ^ { 2 } = - \frac { 1 } { 16 } y$ , focus: $\left( 0 , - \frac { 1 } { 16 } \right)$ 
C)  $x ^ { 2 } = - \frac { 1 } { 4 } y$ , focus: $\left( 0 , - \frac { 1 } { 16 } \right)$ 
D)  $x ^ { 2 } = - 4 y$ , focus: (0,-4) 
E)  $x ^ { 2 } = - \frac { 1 } { 4 } y$ , focus: $\left( 0 , - \frac { 1 } { 4 } \right)$

Question 12

Use the Quadratic Formula to solve for $y$ .  $x ^ { 2 } - 5 x y - 4 y ^ { 2 } + 3 x - 32 = 0$

Accepted Answer

A)  $y = \frac { - 5 x \pm \sqrt { 25 x ^ { 2 } + 16 \left( x ^ { 2 } - 3 x - 32 \right) } } { 8 }$ 
B)  $y = \frac { - 5 x \pm \sqrt { 25 x ^ { 2 } - 16 \left( x ^ { 2 } + 3 x - 32 \right) } } { 8 }$ 
C)  $y = \frac { - 5 x \pm \sqrt { 25 x ^ { 2 } - 16 \left( x ^ { 2 } + 3 x + 32 \right) } } { 8 }$ 
D)  $y = \frac { - 5 x \pm \sqrt { 25 x ^ { 2 } + 16 \left( x ^ { 2 } + 3 x - 32 \right) } } { 8 }$ 
E)  $y = \frac { 5 x \pm \sqrt { 25 x ^ { 2 } + 16 \left( x ^ { 2 } + 3 x - 32 \right) } } { 8 }$ 
A)  $y = \frac { - 5 x \pm \sqrt { 25 x ^ { 2 } + 16 \left( x ^ { 2 } - 3 x - 32 \right) } } { 8 }$ 
B)  $y = \frac { - 5 x \pm \sqrt { 25 x ^ { 2 } - 16 \left( x ^ { 2 } + 3 x - 32 \right) } } { 8 }$ 
C)  $y = \frac { - 5 x \pm \sqrt { 25 x ^ { 2 } - 16 \left( x ^ { 2 } + 3 x + 32 \right) } } { 8 }$ 
D)  $y = \frac { - 5 x \pm \sqrt { 25 x ^ { 2 } + 16 \left( x ^ { 2 } + 3 x - 32 \right) } } { 8 }$ 
E)  $y = \frac { 5 x \pm \sqrt { 25 x ^ { 2 } + 16 \left( x ^ { 2 } + 3 x - 32 \right) } } { 8 }$

Question 13

The revenue R (in dollars) generated by the sale of x units of a patio furniture set is given by $( x - 116 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 16,820 )$ .Approximate the number of sales that will maximize revenue.

Accepted Answer

A)  $R = 116 x - \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 116$ units. 
B)  $R = 116 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 16,820$ units. 
C)  $R = 290 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 16,820$ units. 
D)  $R = 290 x - \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 116$ units. 
E)  $R = 290 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 290$ units. 
A)  $R = 116 x - \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 116$ units. 
B)  $R = 116 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 16,820$ units. 
C)  $R = 290 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 16,820$ units. 
D)  $R = 290 x - \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 116$ units. 
E)  $R = 290 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 290$ units.

Question 14

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $\gamma = ( 1 + \cos \theta )$

Accepted Answer

A) Symmetric with respect to polar axis $$| r | = 2 \text { when } \theta = 0$$
$r = 0$ when $\theta = \pi$    
B) Symmetric with respect to polar axis $$| r | = 2 \text { when } \theta = 0$$
$r = 0$ when $\theta = \pi$    
C) Symmetric with respect to polar axis $$| r | = 2 \text { when } \theta = 0$$
$r = 0$ when $\theta = \pi$   
D) Symmetric with respect to polar axis $$| r | = 2 \text { when } \theta = 0$$
$r = 0$ when $\theta = \pi$    
E) Symmetric with respect to polar axis $$| r | = 2 \text { when } \theta = 0$$
$r = 0$ when $\theta = \pi$   
A) Symmetric with respect to polar axis $$| r | = 2 \text { when } \theta = 0$$
$r = 0$ when $\theta = \pi$    
B) Symmetric with respect to polar axis $$| r | = 2 \text { when } \theta = 0$$
$r = 0$ when $\theta = \pi$    
C) Symmetric with respect to polar axis $$| r | = 2 \text { when } \theta = 0$$
$r = 0$ when $\theta = \pi$   
D) Symmetric with respect to polar axis $$| r | = 2 \text { when } \theta = 0$$
$r = 0$ when $\theta = \pi$    
E) Symmetric with respect to polar axis $$| r | = 2 \text { when } \theta = 0$$
$r = 0$ when $\theta = \pi$

Question 15

Identify the conic and select its correct graph. $r = \frac { 6 } { 1 + \sin \theta }$

Accepted Answer

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

Question 16

The revenue (in dollars) generated by the sale of units of a patio furniture set is given by $( x - 130 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 23,660 )$ .Select the correct graph of the function.

Accepted Answer

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

Question 17

Use the Quadratic Formula to solve for $y$ .  $x ^ { 2 } + 12 x y + 36 y ^ { 2 } - 5 x - y - 3 = 0$

Accepted Answer

A)  $y = \frac { - ( 36 x + 1 ) \pm \sqrt { ( 36 x - 1 ) ^ { 2 } - 144 \left( x ^ { 2 } - 5 x - 3 \right) } } { 72 }$ 
B)  $y = \frac { - ( 12 x + 1 ) \pm \sqrt { ( 36 x + 1 ) ^ { 2 } - 144 \left( x ^ { 2 } + 5 x + 3 \right) } } { 72 }$ 
C)  $y = \frac { - ( 36 x - 1 ) \pm \sqrt { ( 36 x - 1 ) ^ { 2 } - 144 \left( x ^ { 2 } - 5 x + 3 \right) } } { 72 }$ 
D)  $y = \frac { ( 36 x - 1 ) \pm \sqrt { ( 36 x - 1 ) ^ { 2 } - 144 \left( x ^ { 2 } - 5 x - 3 \right) } } { 72 }$ 
E)  $y = \frac { - ( 12 x - 1 ) \pm \sqrt { ( 12 x - 1 ) ^ { 2 } - 144 \left( x ^ { 2 } - 5 x - 3 \right) } } { 72 }$ 
A)  $y = \frac { - ( 36 x + 1 ) \pm \sqrt { ( 36 x - 1 ) ^ { 2 } - 144 \left( x ^ { 2 } - 5 x - 3 \right) } } { 72 }$ 
B)  $y = \frac { - ( 12 x + 1 ) \pm \sqrt { ( 36 x + 1 ) ^ { 2 } - 144 \left( x ^ { 2 } + 5 x + 3 \right) } } { 72 }$ 
C)  $y = \frac { - ( 36 x - 1 ) \pm \sqrt { ( 36 x - 1 ) ^ { 2 } - 144 \left( x ^ { 2 } - 5 x + 3 \right) } } { 72 }$ 
D)  $y = \frac { ( 36 x - 1 ) \pm \sqrt { ( 36 x - 1 ) ^ { 2 } - 144 \left( x ^ { 2 } - 5 x - 3 \right) } } { 72 }$ 
E)  $y = \frac { - ( 12 x - 1 ) \pm \sqrt { ( 12 x - 1 ) ^ { 2 } - 144 \left( x ^ { 2 } - 5 x - 3 \right) } } { 72 }$

Question 18

Convert the rectangular equation to polar form.Assume a > 0, r > 0.  $x ^ { 2 } + y ^ { 2 } - 5 a x = 0$

Accepted Answer

A)  $r = 5 a \sin \theta$ 
B)  $r = 5 a \cot \Theta$ 
C)  $r = 5 \operatorname { acsc } \theta$ 
D)  $r = 5 a \cos \theta$ 
E)  $r = 5 \operatorname { asec } \theta$ 
A)  $r = 5 a \sin \theta$ 
B)  $r = 5 a \cot \Theta$ 
C)  $r = 5 \operatorname { acsc } \theta$ 
D)  $r = 5 a \cos \theta$ 
E)  $r = 5 \operatorname { asec } \theta$

Question 19

Select the correct equation of the following graph.

Accepted Answer

A)  $\frac { ( x - 1 ) ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x - 1 ) ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
D)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = 1$ 
A)  $\frac { ( x - 1 ) ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x - 1 ) ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
D)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = 1$

Question 20

A point (a,b) = (r, $\theta $) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.    $$a = 5 , b = - \pi$$

Accepted Answer

A) Rectangular coordinates: (5,0) 
B) Rectangular coordinates: (5,5) 
C) Rectangular coordinates: (-5,5) 
D) Rectangular coordinates: (-5,0) 
E) Rectangular coordinates: (0,5) 
A) Rectangular coordinates: (5,0) 
B) Rectangular coordinates: (5,5) 
C) Rectangular coordinates: (-5,5) 
D) Rectangular coordinates: (-5,0) 
E) Rectangular coordinates: (0,5)

Find the vertex and focus of the parabola from the given equation and select its graph. $y = \frac { 1 } { 6 } x ^ { 2 }$

Find the equation of the hyperbola with vertices (2, 0), (-2, 0) and focus (4, 0).

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = 2\quad\quad\quad x = 1$

Find the center and vertices of the ellipse. $x ^ { 2 } + 4 y ^ { 2 } - 6 x + 8 y + 9 = 0$

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

Graph the following equation. $x ^ { 2 } - 6 x + y ^ { 2 } = 7$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2 ( 1 - \sin \theta )$

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = \frac { 1 } { 2 } \quad\quad\quad y = 3$

Using following result find a set of parametric equation of conic. Hyperbola: $x = h + a \sec \theta , y = k + b \tan \theta$ Hyperbola: vertices: $( \pm 15,0 )$ ; foci: $( \pm 17,0 )$

Convert the polar equation to rectangular form. $r = - 5 \cos \theta$

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

Use the Quadratic Formula to solve for $y$ . $x ^ { 2 } - 5 x y - 4 y ^ { 2 } + 3 x - 32 = 0$

The revenue R (in dollars) generated by the sale of x units of a patio furniture set is given by $( x - 116 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 16,820 )$ .Approximate the number of sales that will maximize revenue.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $\gamma = ( 1 + \cos \theta )$

Identify the conic and select its correct graph. $r = \frac { 6 } { 1 + \sin \theta }$

The revenue (in dollars) generated by the sale of units of a patio furniture set is given by $( x - 130 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 23,660 )$ .Select the correct graph of the function.

Use the Quadratic Formula to solve for $y$ . $x ^ { 2 } + 12 x y + 36 y ^ { 2 } - 5 x - y - 3 = 0$

Convert the rectangular equation to polar form.Assume a > 0, r > 0. $x ^ { 2 } + y ^ { 2 } - 5 a x = 0$

Select the correct equation of the following graph.

A point (a,b) = (r, $\theta$ ) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. $A point (a,b) = (r, \theta ) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a = 5 , b = - \pi$ $a = 5 , b = - \pi$

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Exam 10: Topics In Analytic Geometry

Find the vertex and focus of the parabola from the given equation and select its graph. y=16x2y = \frac { 1 } { 6 } x ^ { 2 }y=61​x2

Find the equation of the hyperbola with vertices (2, 0), (-2, 0) and focus (4, 0).

Find a polar equation of the conic with its focus at the pole. Conics \quad\quad Eccentricity \quad\quad Directrix Ellipse e=2x=1\quad\quad\quad e = 2\quad\quad\quad x = 1e=2x=1

Find the center and vertices of the ellipse. x2+4y2−6x+8y+9=0x ^ { 2 } + 4 y ^ { 2 } - 6 x + 8 y + 9 = 0x2+4y2−6x+8y+9=0

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

Graph the following equation. x2−6x+y2=7x ^ { 2 } - 6 x + y ^ { 2 } = 7x2−6x+y2=7

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=2(1−sin⁡θ)r = 2 ( 1 - \sin \theta )r=2(1−sinθ)

Find a polar equation of the conic with its focus at the pole. Conics \quad\quad Eccentricity \quad\quad Directrix Ellipse e=12y=3\quad\quad\quad e = \frac { 1 } { 2 } \quad\quad\quad y = 3e=21​y=3

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: (±15,0)( \pm 15,0 )(±15,0) ; foci: (±17,0)( \pm 17,0 )(±17,0)

Convert the polar equation to rectangular form. r=−5cos⁡θr = - 5 \cos \thetar=−5cosθ

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

Use the Quadratic Formula to solve for yyy . x2−5xy−4y2+3x−32=0x ^ { 2 } - 5 x y - 4 y ^ { 2 } + 3 x - 32 = 0x2−5xy−4y2+3x−32=0

The revenue R (in dollars) generated by the sale of x units of a patio furniture set is given by (x−116)2=−45(R−16,820)( x - 116 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 16,820 )(x−116)2=−54​(R−16,820) .Approximate the number of sales that will maximize revenue.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. γ=(1+cos⁡θ)\gamma = ( 1 + \cos \theta )γ=(1+cosθ)

Identify the conic and select its correct graph. r=61+sin⁡θr = \frac { 6 } { 1 + \sin \theta }r=1+sinθ6​

The revenue (in dollars) generated by the sale of units of a patio furniture set is given by (x−130)2=−57(R−23,660)( x - 130 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 23,660 )(x−130)2=−75​(R−23,660) .Select the correct graph of the function.

Use the Quadratic Formula to solve for yyy . x2+12xy+36y2−5x−y−3=0x ^ { 2 } + 12 x y + 36 y ^ { 2 } - 5 x - y - 3 = 0x2+12xy+36y2−5x−y−3=0

Convert the rectangular equation to polar form.Assume a > 0, r > 0. x2+y2−5ax=0x ^ { 2 } + y ^ { 2 } - 5 a x = 0x2+y2−5ax=0

Select the correct equation of the following graph.

A point (a,b) = (r, θ\theta θ ) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a=5,b=−πa = 5 , b = - \pia=5,b=−π

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Find the vertex and focus of the parabola from the given equation and select its graph. $y = \frac { 1 } { 6 } x ^ { 2 }$

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = 2\quad\quad\quad x = 1$

Find the center and vertices of the ellipse. $x ^ { 2 } + 4 y ^ { 2 } - 6 x + 8 y + 9 = 0$

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

Graph the following equation. $x ^ { 2 } - 6 x + y ^ { 2 } = 7$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2 ( 1 - \sin \theta )$

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = \frac { 1 } { 2 } \quad\quad\quad y = 3$

Using following result find a set of parametric equation of conic. Hyperbola: $x = h + a \sec \theta , y = k + b \tan \theta$ Hyperbola: vertices: $( \pm 15,0 )$ ; foci: $( \pm 17,0 )$

Convert the polar equation to rectangular form. $r = - 5 \cos \theta$

Use the Quadratic Formula to solve for $y$ . $x ^ { 2 } - 5 x y - 4 y ^ { 2 } + 3 x - 32 = 0$

The revenue R (in dollars) generated by the sale of x units of a patio furniture set is given by $( x - 116 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 16,820 )$ .Approximate the number of sales that will maximize revenue.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $\gamma = ( 1 + \cos \theta )$

Identify the conic and select its correct graph. $r = \frac { 6 } { 1 + \sin \theta }$

The revenue (in dollars) generated by the sale of units of a patio furniture set is given by $( x - 130 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 23,660 )$ .Select the correct graph of the function.

Use the Quadratic Formula to solve for $y$ . $x ^ { 2 } + 12 x y + 36 y ^ { 2 } - 5 x - y - 3 = 0$

Convert the rectangular equation to polar form.Assume a > 0, r > 0. $x ^ { 2 } + y ^ { 2 } - 5 a x = 0$

A point (a,b) = (r, $\theta$ ) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. $A point (a,b) = (r, \theta ) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a = 5 , b = - \pi$ $a = 5 , b = - \pi$