Question 1

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. 
Vertical axis and passes through the point (6,8)

Accepted Answer

A)  $x ^ { 2 } = \frac { 36 } { 8 } y$ 
B)  $y ^ { 2 } = \frac { 8 } { 36 } x$ 
C)  $x ^ { 2 } = \frac { 8 } { 36 } y$ 
D)  $y ^ { 2 } = x$ 
E)  $y ^ { 2 } = \frac { 36 } { 8 } x$ 
A)  $x ^ { 2 } = \frac { 36 } { 8 } y$ 
B)  $y ^ { 2 } = \frac { 8 } { 36 } x$ 
C)  $x ^ { 2 } = \frac { 8 } { 36 } y$ 
D)  $y ^ { 2 } = x$ 
E)  $y ^ { 2 } = \frac { 36 } { 8 } x$

Question 2

Convert the rectangular equation to polar form.Assume r > 1.  $x y = 13$

Accepted Answer

A)  $r ^ { 2 } = 13 \sec 2 \theta$ 
B)  $r ^ { 2 } = 26 \csc 2 \theta$ 
C)  $r ^ { 2 } = 26 \cos 2 \theta$ 
D)  $r ^ { 2 } = 13 \csc 2 \theta$ 
E)  $r ^ { 2 } = 26 \sec 2 \Theta$ 
A)  $r ^ { 2 } = 13 \sec 2 \theta$ 
B)  $r ^ { 2 } = 26 \csc 2 \theta$ 
C)  $r ^ { 2 } = 26 \cos 2 \theta$ 
D)  $r ^ { 2 } = 13 \csc 2 \theta$ 
E)  $r ^ { 2 } = 26 \sec 2 \Theta$

Question 3

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $3 x ^ { 2 } - 9 x y + 11 y ^ { 2 } + ( 3 \sqrt { 10 } - 9 ) x - ( 5 \sqrt { 10 } + 10 ) y = 91$

Accepted Answer

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

Question 4

Find the vertex, focus, and directrix of the parabola.  $x ^ { 2 } + 4 y = 0$

Accepted Answer

A) Vertex: (0,0); Focus: $\left( \frac { 1 } { 4 } , 0 \right)$ ; Directrix: $y = \frac { 1 } { 4 }$ 
B) Vertex: (0,0); Focus: $\left( - \frac { 1 } { 4 } , 0 \right)$ ; Directrix: $y = \frac { 1 } { 4 }$ 
C) Vertex: (0,0): Focus: $\left( 0 , \frac { 4 } { 4 } \right)$ Directrix: $y = - \frac { 4 } { 4 }$ 
D) Vertex: (0,0); Focus: $\left( 0 , - \frac { 4 } { 4 } \right)$ ; Directrix: $y = \frac { 4 } { 4 }$ 
E) Vertex: (0,0); Focus: $\left( 0 , - \frac { 4 } { 4 } \right)$ ; Directrix: $y = - \frac { 4 } { 4 }$ 
A) Vertex: (0,0); Focus: $\left( \frac { 1 } { 4 } , 0 \right)$ ; Directrix: $y = \frac { 1 } { 4 }$ 
B) Vertex: (0,0); Focus: $\left( - \frac { 1 } { 4 } , 0 \right)$ ; Directrix: $y = \frac { 1 } { 4 }$ 
C) Vertex: (0,0): Focus: $\left( 0 , \frac { 4 } { 4 } \right)$ Directrix: $y = - \frac { 4 } { 4 }$ 
D) Vertex: (0,0); Focus: $\left( 0 , - \frac { 4 } { 4 } \right)$ ; Directrix: $y = \frac { 4 } { 4 }$ 
E) Vertex: (0,0); Focus: $\left( 0 , - \frac { 4 } { 4 } \right)$ ; Directrix: $y = - \frac { 4 } { 4 }$

Question 5

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola.  $\frac { ( x + 5 ) ^ { 2 } } { 121 } - \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$

Accepted Answer

A) Center: $( - 5,4 )$    
B) Center: (5, 4)   
C) Center: (0, 0)   
D) Center: $( - 5 , - 4 )$   
E) Center: (0, 0)   
A) Center: $( - 5,4 )$    
B) Center: (5, 4)   
C) Center: (0, 0)   
D) Center: $( - 5 , - 4 )$   
E) Center: (0, 0)

Question 6

Identify the graph of the following ellipse.  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 1$

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.
 $r = 4 \sin 3 \theta$

Accepted Answer

A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { c } 
| r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \
r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }
\end{array}$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { c } 
| r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \
r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }
\end{array}$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { c } 
| r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \
r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }
\end{array}$    
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { c } 
| r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \
r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }
\end{array}$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { c } 
| r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \
r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }
\end{array}$    
A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { c } 
| r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \
r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }
\end{array}$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { c } 
| r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \
r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }
\end{array}$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { c } 
| r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \
r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }
\end{array}$    
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { c } 
| r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \
r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }
\end{array}$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { c } 
| r | = 4 \text { when } \theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \
r = 0 \text { when } \theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }
\end{array}$

Question 8

Select the curve represented by the parametric equations. 
Prolate cycloid: $x = \Theta - \frac { 4 } { 3 } \sin \Theta , y = 1 - \frac { 4 } { 3 } \cos \Theta $

Accepted Answer

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

Question 9

Use the discriminant to classify the graph.  $36 x ^ { 2 } - 144 x y + y ^ { 2 } - 10 x + 5 y = 0$

Accepted Answer

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

Question 10

Identify the conic by writing the equation in standard form.  $25 x ^ { 2 } + 4 y ^ { 2 } - 400 x + 72 y + 1824 = 0$

Accepted Answer

A)  $\frac { ( x + 4 ) ^ { 2 } } { \frac { 4 } { 8 } } + \frac { ( y - 8 ) ^ { 2 } } { \frac { 8 } { 4 } } = 1$ ; ellipse 
B)  $\frac { ( x - 8 ) ^ { 2 } } { \frac { 8 } { 4 } } + \frac { ( y + 4 ) ^ { 2 } } { \frac { 8 } { 4 } } = 1$ ; ellipse 
C)  $\frac { ( x - 8 ) ^ { 2 } } { \frac { 4 } { 8 } } + \frac { ( y + 4 ) ^ { 2 } } { \frac { 8 } { 4 } } = 1$ ; ellipse 
D)  $\frac { ( x - 8 ) ^ { 2 } } { 4 } + \frac { ( y + 9 ) ^ { 2 } } { 25 } = 1$ ; ellipse 
E)  $( 5 x - 8 ) ^ { 2 } + ( 2 y + 9 ) ^ { 2 } = - 1783$ ; circle 
A)  $\frac { ( x + 4 ) ^ { 2 } } { \frac { 4 } { 8 } } + \frac { ( y - 8 ) ^ { 2 } } { \frac { 8 } { 4 } } = 1$ ; ellipse 
B)  $\frac { ( x - 8 ) ^ { 2 } } { \frac { 8 } { 4 } } + \frac { ( y + 4 ) ^ { 2 } } { \frac { 8 } { 4 } } = 1$ ; ellipse 
C)  $\frac { ( x - 8 ) ^ { 2 } } { \frac { 4 } { 8 } } + \frac { ( y + 4 ) ^ { 2 } } { \frac { 8 } { 4 } } = 1$ ; ellipse 
D)  $\frac { ( x - 8 ) ^ { 2 } } { 4 } + \frac { ( y + 9 ) ^ { 2 } } { 25 } = 1$ ; ellipse 
E)  $( 5 x - 8 ) ^ { 2 } + ( 2 y + 9 ) ^ { 2 } = - 1783$ ; circle

Question 11

Find a set of parametric equations for the rectangular equation.  $\begin{array} { l } 
t = 2 - x \
x = 5 y - 2
\end{array}$

Accepted Answer

A)  $x = 5 + t , y = \frac { 1 } { 2 } ( 4 - t )$ 
B)  $x = 2 - t , y = \frac { 1 } { 5 } ( 4 - t )$ 
C)  $x = 2 + t , y = \frac { 1 } { 5 } ( 4 - t )$ 
D)  $x = 2 + t , y = \frac { 1 } { 5 } ( 4 + t )$ 
E)  $x = 2 + t , y = \frac { 1 } { 5 } ( t - 4 )$ 
A)  $x = 5 + t , y = \frac { 1 } { 2 } ( 4 - t )$ 
B)  $x = 2 - t , y = \frac { 1 } { 5 } ( 4 - t )$ 
C)  $x = 2 + t , y = \frac { 1 } { 5 } ( 4 - t )$ 
D)  $x = 2 + t , y = \frac { 1 } { 5 } ( 4 + t )$ 
E)  $x = 2 + t , y = \frac { 1 } { 5 } ( t - 4 )$

Question 12

Consider the equation.  $10 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 81 = 0$ 
Explain how to identify the graph of the equation.

Accepted Answer

A) Find the discriminant of the equation to identify the graph of the equation. 
B) Find the foci of the equation to identify the graph of the equation. 
C) Find the major axis of the equation to identify the graph of the equation. 
D) Find the minor axis of the equation to identify the graph of the equation. 
E) Find the vertices of the equation to identify the graph of the equation. 
A) Find the discriminant of the equation to identify the graph of the equation. 
B) Find the foci of the equation to identify the graph of the equation. 
C) Find the major axis of the equation to identify the graph of the equation. 
D) Find the minor axis of the equation to identify the graph of the equation. 
E) Find the vertices of the equation to identify the graph of the equation.

Question 13

Give the standard form of the equation of the parabola with the given characteristics. vertex: (7, 8) focus: (5, 8)

Accepted Answer

A)  $( y + 8 ) ^ { 2 } = - 8 ( x + 7 )$ 
B)  $( y - 8 ) ^ { 2 } = - 8 ( x - 7 )$ 
C)  $( x + 7 ) ^ { 2 } = 8 ( y + 8 )$ 
D)  $( y - 8 ) ^ { 2 } = 8 ( x - 7 )$ 
E)  $( x - 7 ) ^ { 2 } = 8 ( y - 8 )$ 
A)  $( y + 8 ) ^ { 2 } = - 8 ( x + 7 )$ 
B)  $( y - 8 ) ^ { 2 } = - 8 ( x - 7 )$ 
C)  $( x + 7 ) ^ { 2 } = 8 ( y + 8 )$ 
D)  $( y - 8 ) ^ { 2 } = 8 ( x - 7 )$ 
E)  $( x - 7 ) ^ { 2 } = 8 ( y - 8 )$

Question 14

Match the equation with its graph. $x ^ { 2 } + 4 y ^ { 2 } = 4$

Accepted Answer

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

Question 15

Give the coordinates of the circle's center and it radius.
  $( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1$  
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 16

Select the graph of the conic.  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 1$

Accepted Answer

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

Question 17

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0.  $( 0,4 )$

Accepted Answer

A) Polar coordinates: $\left( 4 , - \frac { \pi } { 2 } \right)$ 
B) Polar coordinates: $\left( - 4 , - \frac { \pi } { 2 } \right)$ 
C) Polar coordinates: $\left( 4 , \frac { \pi } { 2 } \right)$ 
D) Polar coordinates: $\left( - 4 , \frac { 3 \pi } { 2 } \right)$ 
E) Polar coordinates: $\left( 4 , \frac { 3 \pi } { 2 } \right)$ 
A) Polar coordinates: $\left( 4 , - \frac { \pi } { 2 } \right)$ 
B) Polar coordinates: $\left( - 4 , - \frac { \pi } { 2 } \right)$ 
C) Polar coordinates: $\left( 4 , \frac { \pi } { 2 } \right)$ 
D) Polar coordinates: $\left( - 4 , \frac { 3 \pi } { 2 } \right)$ 
E) Polar coordinates: $\left( 4 , \frac { 3 \pi } { 2 } \right)$

Question 18

Find the distance between the point and the line.Round your answer to four decimal places.  Point Line
$$( 9,8 ) - 8 x + y - 8 = 0$$

Accepted Answer

A)  $d \approx 9.0554$ 
B)  $d \approx 10.0554$ 
C)  $d \approx 11.0554$ 
D)  $d \approx 8.0554$ 
E)  $d \approx 12.0554$ 
A)  $d \approx 9.0554$ 
B)  $d \approx 10.0554$ 
C)  $d \approx 11.0554$ 
D)  $d \approx 8.0554$ 
E)  $d \approx 12.0554$

Question 19

Select the curve represented by the parametric equations.  $x = \sqrt { t }$ $y = 1 - t$

Accepted Answer

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

Question 20

Find a polar equation of the conic with its focus at the pole. 
Conics $\quad$$\quad$Vertex or vertices
Parabola$\quad$ $\quad ( 10 , \pi / 2 )$

Accepted Answer

A)  $\frac { 20 } { 1 - \sin \theta }$ 
B)  $\frac { 20 } { 1 + \sin \theta }$ 
C)  $\frac { 20 } { 1 - \cos \theta }$ 
D)  $\frac { 20 } { 1 + \cos \theta }$ 
E)  $\frac { - 20 } { 1 - \sin \theta }$ 
A)  $\frac { 20 } { 1 - \sin \theta }$ 
B)  $\frac { 20 } { 1 + \sin \theta }$ 
C)  $\frac { 20 } { 1 - \cos \theta }$ 
D)  $\frac { 20 } { 1 + \cos \theta }$ 
E)  $\frac { - 20 } { 1 - \sin \theta }$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Vertical axis and passes through the point (6,8)

Convert the rectangular equation to polar form.Assume r > 1. $x y = 13$

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $3 x ^ { 2 } - 9 x y + 11 y ^ { 2 } + ( 3 \sqrt { 10 } - 9 ) x - ( 5 \sqrt { 10 } + 10 ) y = 91$

Find the vertex, focus, and directrix of the parabola. $x ^ { 2 } + 4 y = 0$

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola. $\frac { ( x + 5 ) ^ { 2 } } { 121 } - \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$

Identify the graph of the following ellipse. $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 1$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 4 \sin 3 \theta$

Select the curve represented by the parametric equations. Prolate cycloid: $x = \Theta - \frac { 4 } { 3 } \sin \Theta , y = 1 - \frac { 4 } { 3 } \cos \Theta$

Use the discriminant to classify the graph. $36 x ^ { 2 } - 144 x y + y ^ { 2 } - 10 x + 5 y = 0$

Identify the conic by writing the equation in standard form. $25 x ^ { 2 } + 4 y ^ { 2 } - 400 x + 72 y + 1824 = 0$

Find a set of parametric equations for the rectangular equation. t=2-x x=5y-2

Consider the equation. $10 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 81 = 0$ Explain how to identify the graph of the equation.

Give the standard form of the equation of the parabola with the given characteristics. vertex: (7, 8) focus: (5, 8)

Match the equation with its graph. $x ^ { 2 } + 4 y ^ { 2 } = 4$

Give the coordinates of the circle's center and it radius. $( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1$ Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

Select the graph of the conic. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 1$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( 0,4 )$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 9,8 ) - 8 x + y - 8 = 0$

Select the curve represented by the parametric equations. $x = \sqrt { t }$ $y = 1 - t$

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Vertex or vertices Parabola $\quad$ $\quad ( 10 , \pi / 2 )$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

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Additional Topics In Trigonometery

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Limits and An Introduction To Calculus

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Exam 10: Topics In Analytic Geometry

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Vertical axis and passes through the point (6,8)

Convert the rectangular equation to polar form.Assume r > 1. xy=13x y = 13xy=13

Determine the angle θ\thetaθ through which the axes are rotated.Round your answer to two decimal places. 3x2−9xy+11y2+(310−9)x−(510+10)y=913 x ^ { 2 } - 9 x y + 11 y ^ { 2 } + ( 3 \sqrt { 10 } - 9 ) x - ( 5 \sqrt { 10 } + 10 ) y = 913x2−9xy+11y2+(310​−9)x−(510​+10)y=91

Find the vertex, focus, and directrix of the parabola. x2+4y=0x ^ { 2 } + 4 y = 0x2+4y=0

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola. (x+5)2121−(y−4)225=1\frac { ( x + 5 ) ^ { 2 } } { 121 } - \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1121(x+5)2​−25(y−4)2​=1

Identify the graph of the following ellipse. x236+y24=1\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 136x2​+4y2​=1

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=4sin⁡3θr = 4 \sin 3 \thetar=4sin3θ

Select the curve represented by the parametric equations. Prolate cycloid: x=Θ−43sin⁡Θ,y=1−43cos⁡Θx = \Theta - \frac { 4 } { 3 } \sin \Theta , y = 1 - \frac { 4 } { 3 } \cos \Theta x=Θ−34​sinΘ,y=1−34​cosΘ

Use the discriminant to classify the graph. 36x2−144xy+y2−10x+5y=036 x ^ { 2 } - 144 x y + y ^ { 2 } - 10 x + 5 y = 036x2−144xy+y2−10x+5y=0

Identify the conic by writing the equation in standard form. 25x2+4y2−400x+72y+1824=025 x ^ { 2 } + 4 y ^ { 2 } - 400 x + 72 y + 1824 = 025x2+4y2−400x+72y+1824=0

Find a set of parametric equations for the rectangular equation. t=2-x x=5y-2

Consider the equation. 10x2−5xy+10y2−81=010 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 81 = 010x2−5xy+10y2−81=0 Explain how to identify the graph of the equation.

Give the standard form of the equation of the parabola with the given characteristics. vertex: (7, 8) focus: (5, 8)

Match the equation with its graph. x2+4y2=4x ^ { 2 } + 4 y ^ { 2 } = 4x2+4y2=4

Give the coordinates of the circle's center and it radius. (x−4)2+(y+3)2=1( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1(x−4)2+(y+3)2=1 Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

Select the graph of the conic. x264+y264=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 164x2​+64y2​=1

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. (0,4)( 0,4 )(0,4)

Find the distance between the point and the line.Round your answer to four decimal places. Point Line (9,8)−8x+y−8=0( 9,8 ) - 8 x + y - 8 = 0(9,8)−8x+y−8=0

Select the curve represented by the parametric equations. x=tx = \sqrt { t }x=t​ y=1−ty = 1 - ty=1−t

Find a polar equation of the conic with its focus at the pole. Conics \quad\quad Vertex or vertices Parabola \quad (10,π/2)\quad ( 10 , \pi / 2 )(10,π/2)

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 r > 1. $x y = 13$

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $3 x ^ { 2 } - 9 x y + 11 y ^ { 2 } + ( 3 \sqrt { 10 } - 9 ) x - ( 5 \sqrt { 10 } + 10 ) y = 91$

Find the vertex, focus, and directrix of the parabola. $x ^ { 2 } + 4 y = 0$

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola. $\frac { ( x + 5 ) ^ { 2 } } { 121 } - \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$

Identify the graph of the following ellipse. $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 1$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 4 \sin 3 \theta$

Select the curve represented by the parametric equations. Prolate cycloid: $x = \Theta - \frac { 4 } { 3 } \sin \Theta , y = 1 - \frac { 4 } { 3 } \cos \Theta$

Use the discriminant to classify the graph. $36 x ^ { 2 } - 144 x y + y ^ { 2 } - 10 x + 5 y = 0$

Identify the conic by writing the equation in standard form. $25 x ^ { 2 } + 4 y ^ { 2 } - 400 x + 72 y + 1824 = 0$

Consider the equation. $10 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 81 = 0$ Explain how to identify the graph of the equation.

Match the equation with its graph. $x ^ { 2 } + 4 y ^ { 2 } = 4$

Give the coordinates of the circle's center and it radius. $( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1$ Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

Select the graph of the conic. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 1$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( 0,4 )$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 9,8 ) - 8 x + y - 8 = 0$

Select the curve represented by the parametric equations. $x = \sqrt { t }$ $y = 1 - t$

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Vertex or vertices Parabola $\quad$ $\quad ( 10 , \pi / 2 )$