Question 1

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places.  $48 x ^ { 2 } + 69 x y + 25 y ^ { 2 } = 50$

Accepted Answer

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

Question 2

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 5).

Accepted Answer

A)  $x ^ { 2 } = 20 y$ 
B)  $x ^ { 2 } = 5 y$ 
C)  $y ^ { 2 } = 20 x$ 
D)  $x ^ { 2 } = y + 5$ 
E) none of these 
A)  $x ^ { 2 } = 20 y$ 
B)  $x ^ { 2 } = 5 y$ 
C)  $y ^ { 2 } = 20 x$ 
D)  $x ^ { 2 } = y + 5$ 
E) none of these

Question 3

Select the correct graph of the following equations of the hyperbola and find the center of hyperbola.  $\frac { ( x - 6 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { 1 } = 1$

Accepted Answer

A) Center: (0, 0)   
B) Center: (0, 0)   
C) Center: $( 6,2 )$    
D) Center:(0,0)  
E) Center: $( 6 , - 2 )$    
A) Center: (0, 0)   
B) Center: (0, 0)   
C) Center: $( 6,2 )$    
D) Center:(0,0)  
E) Center: $( 6 , - 2 )$

Question 4

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).   L = 5 inches 
Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Accepted Answer

A)  $y = \frac { 1 } { 5 } x ^ { 2 }$ 
B)  $y = 5 x ^ { 2 }$ 
C)  $y = 20 x ^ { 2 }$ 
D)  $x ^ { 2 } = 20 y$ 
E)  $x ^ { 2 } = 5 y$ 
A)  $y = \frac { 1 } { 5 } x ^ { 2 }$ 
B)  $y = 5 x ^ { 2 }$ 
C)  $y = 20 x ^ { 2 }$ 
D)  $x ^ { 2 } = 20 y$ 
E)  $x ^ { 2 } = 5 y$

Question 5

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.  $25 x ^ { 2 } + 64 y ^ { 2 } - 14 x + 17 y - 119 = 0$

Accepted Answer

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

Question 6

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. 
Foci: $( \pm 2,0 )$ ; major axis of length 18

Accepted Answer

A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 77 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 2 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 77 } = 1$ 
D)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 4 } = 1$ 
E)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 77 } = 1$ 
A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 77 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 2 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 77 } = 1$ 
D)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 4 } = 1$ 
E)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 77 } = 1$

Question 7

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. $\theta = 45 ^ { \circ }$ , $( 10,10 )$

Accepted Answer

A)  $( - 5 \sqrt { 2 } , 0 )$ 
B)  $( 5 \sqrt { 2 } , 0 )$ 
C)  $( - 10 \sqrt { 2 } , 0 )$ 
D)  $( 6 \sqrt { 2 } , 0 )$ 
E)  $( 10 \sqrt { 2 } , 0 )$ 
A)  $( - 5 \sqrt { 2 } , 0 )$ 
B)  $( 5 \sqrt { 2 } , 0 )$ 
C)  $( - 10 \sqrt { 2 } , 0 )$ 
D)  $( 6 \sqrt { 2 } , 0 )$ 
E)  $( 10 \sqrt { 2 } , 0 )$

Question 8

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

Accepted Answer

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

Question 9

Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance) shown in the picture.    d = 2.25 inches

Accepted Answer

A)  $x ^ { 2 } = 9 y$ 
B)  $y ^ { 2 } = \frac { 1 } { 9 } x$ 
C)  $x ^ { 2 } = 2.25 y$ 
D)  $y ^ { 2 } = 2.25 x$ 
E)  $y ^ { 2 } = 9 x$ 
A)  $x ^ { 2 } = 9 y$ 
B)  $y ^ { 2 } = \frac { 1 } { 9 } x$ 
C)  $x ^ { 2 } = 2.25 y$ 
D)  $y ^ { 2 } = 2.25 x$ 
E)  $y ^ { 2 } = 9 x$

Question 10

Find the lengths of the major and minor axes of the ellipse graphed by following equation.  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 1 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1$

Accepted Answer

A) Length of major axis is $2 a = 2 \cdot ( - 1 ) = - 2$ Length of minor axis is $2 b = 2 \cdot ( - 6 ) = - 12$ 
B) Length of major axis is $2 a = 2 \cdot 1 = 2$ Length of minor axis is $2 b = 2 \cdot 6 = 12$ 
C) Length of major axis is $2 a = 2 \cdot ( - 6 ) = - 12$ Length of minor axis is $2 b = 2 \cdot ( - 1 ) = - 2$ 
D) Length of major axis is $2 a = 2 \cdot 6 = 12$ Length of minor axis is $2 b = 2 \cdot 1 = 2$ 
E) None of the above 
A) Length of major axis is $2 a = 2 \cdot ( - 1 ) = - 2$ Length of minor axis is $2 b = 2 \cdot ( - 6 ) = - 12$ 
B) Length of major axis is $2 a = 2 \cdot 1 = 2$ Length of minor axis is $2 b = 2 \cdot 6 = 12$ 
C) Length of major axis is $2 a = 2 \cdot ( - 6 ) = - 12$ Length of minor axis is $2 b = 2 \cdot ( - 1 ) = - 2$ 
D) Length of major axis is $2 a = 2 \cdot 6 = 12$ Length of minor axis is $2 b = 2 \cdot 1 = 2$ 
E) None of the above

Question 11

Convert the rectangular equation to polar form.Assume r > 1. $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 9 \left( x ^ { 2 } - y ^ { 2 } \right)$

Accepted Answer

A)  $r ^ { 2 } = 9 \cos 2 \theta$ 
B)  $r ^ { 2 } = 9 \csc 2 \theta$ 
C)  $r ^ { 2 } = 9 \cos \theta$ 
D)  $r ^ { 2 } = 9 \sin 2 \theta$ 
E)  $r ^ { 2 } = 9 \sin \theta$ 
A)  $r ^ { 2 } = 9 \cos 2 \theta$ 
B)  $r ^ { 2 } = 9 \csc 2 \theta$ 
C)  $r ^ { 2 } = 9 \cos \theta$ 
D)  $r ^ { 2 } = 9 \sin 2 \theta$ 
E)  $r ^ { 2 } = 9 \sin \theta$

Question 12

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. 
Directrix: y = -1

Accepted Answer

A)  $y ^ { 2 } = 4 x$ 
B)  $x ^ { 2 } = - \frac { y } { 4 }$ 
C)  $x ^ { 2 } = 4 y$ 
D)  $y ^ { 2 } = - 4 x$ 
E)  $x ^ { 2 } = - 4 y$ 
A)  $y ^ { 2 } = 4 x$ 
B)  $x ^ { 2 } = - \frac { y } { 4 }$ 
C)  $x ^ { 2 } = 4 y$ 
D)  $y ^ { 2 } = - 4 x$ 
E)  $x ^ { 2 } = - 4 y$

Question 13

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
$r = 5 \cos \theta$

Accepted Answer

A) Symmetric with respect to polar axisCircle with radius 2.5   
B) Symmetric with respect to polar axisCircle with radius 2.5   
C) Symmetric with respect to polar axisCircle with radius 2.5   
D) Symmetric with respect to polar axisCircle with radius 2.5   
E) Symmetric with respect to polar axisCircle with radius 2.5   
A) Symmetric with respect to polar axisCircle with radius 2.5   
B) Symmetric with respect to polar axisCircle with radius 2.5   
C) Symmetric with respect to polar axisCircle with radius 2.5   
D) Symmetric with respect to polar axisCircle with radius 2.5   
E) Symmetric with respect to polar axisCircle with radius 2.5

Question 14

Find the standard form of the equation of the ellipse with the given characteristics. 
Foci: $( 0,0 ) , ( 6,0 )$ ; major axis of length 10.

Accepted Answer

A)  $\frac { ( x - 3 ) ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x - 3 ) ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x + 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x - 3 ) ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { ( x + 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ 
A)  $\frac { ( x - 3 ) ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x - 3 ) ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x + 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x - 3 ) ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { ( x + 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Question 15

Find the equation of the circle graphed below.

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = 6$ 
B)  $y ^ { 2 } = x ^ { 2 } + 36$ 
C)  $x ^ { 2 } + y ^ { 2 } = 36$ 
D)  $x ^ { 2 } + y ^ { 2 } = 1$ 
E)  $x ^ { 2 } + y = 36$ 
A)  $x ^ { 2 } + y ^ { 2 } = 6$ 
B)  $y ^ { 2 } = x ^ { 2 } + 36$ 
C)  $x ^ { 2 } + y ^ { 2 } = 36$ 
D)  $x ^ { 2 } + y ^ { 2 } = 1$ 
E)  $x ^ { 2 } + y = 36$

Question 16

Find the center and vertices of the hyperbola. $12 x ^ { 2 } - 4 y ^ { 2 } - 72 x - 16 y + 44 = 0$

Accepted Answer

A) center: (3, -2), vertices: (3, -4), (3, 0) 
B) center: (-3, 2), vertices: (-3, 0), (-3, 4) 
C) center: (3, -2), vertices: (1, -2), (5,-2) 
D) center: (2, -3), vertices: (0, -3), (4, -3) 
E) center: (-3,2), vertices: (-5, 2), (-1, 2) 
A) center: (3, -2), vertices: (3, -4), (3, 0) 
B) center: (-3, 2), vertices: (-3, 0), (-3, 4) 
C) center: (3, -2), vertices: (1, -2), (5,-2) 
D) center: (2, -3), vertices: (0, -3), (4, -3) 
E) center: (-3,2), vertices: (-5, 2), (-1, 2)

Question 17

Find the center and foci of the ellipse.  $\frac { ( x - 7 ) ^ { 2 } } { 55 } + \frac { ( y - 2 ) ^ { 2 } } { 64 } = 1$

Accepted Answer

A) center: (-7, -2); foci: (-7, -5), (-7, 1) 
B) center: (7, 2); foci: (-10, -2), (-4, -2) 
C) center: (-7, -2); foci: (-10, 2), (-4, 2) 
D) center: (7, 2); foci: (7, -1), (7, 5) 
E) center: (7, 2); foci: (4, 2), (10, 2) 
A) center: (-7, -2); foci: (-7, -5), (-7, 1) 
B) center: (7, 2); foci: (-10, -2), (-4, -2) 
C) center: (-7, -2); foci: (-10, 2), (-4, 2) 
D) center: (7, 2); foci: (7, -1), (7, 5) 
E) center: (7, 2); foci: (4, 2), (10, 2)

Question 18

Find the slope of the line with inclination $\Theta$ .Round your answer to four decimal places. 
 $\Theta = 2.40 \text { radians }$

Accepted Answer

A)  $m \approx - 1.0160$ 
B)  $m \approx - 1.1160$ 
C)  $m \approx - 1.2160$ 
D)  $m \approx - 0.9160$ 
E)  $m \approx - 1.3160$ 
A)  $m \approx - 1.0160$ 
B)  $m \approx - 1.1160$ 
C)  $m \approx - 1.2160$ 
D)  $m \approx - 0.9160$ 
E)  $m \approx - 1.3160$

Question 19

A straight road rises with an inclination of 0.21 radian from the horizontal (see figure).Find the slope of the road and the change in elevation (x) over a two-mile stretch of the road.Round your answer to four decimal places for the m round your answers to nearest whole number for change in elevation.    $a = 2 , b = 0.21$

Accepted Answer

A)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,203 \text { feet }
\end{array}$ 
B)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,202 \text { feet }
\end{array}$ 
C)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,200 \text { feet }
\end{array}$ 
D)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,199 \text { feet }
\end{array}$ 
E)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,201 \text { feet }
\end{array}$ 
A)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,203 \text { feet }
\end{array}$ 
B)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,202 \text { feet }
\end{array}$ 
C)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,200 \text { feet }
\end{array}$ 
D)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,199 \text { feet }
\end{array}$ 
E)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,201 \text { feet }
\end{array}$

Question 20

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.  $3 y ^ { 2 } + 3 x ^ { 2 } - 21 x + 34 = 0$

Accepted Answer

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

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $48 x ^ { 2 } + 69 x y + 25 y ^ { 2 } = 50$

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 5).

Select the correct graph of the following equations of the hyperbola and find the center of hyperbola. $\frac { ( x - 6 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { 1 } = 1$

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure). L = 5 inches Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $25 x ^ { 2 } + 64 y ^ { 2 } - 14 x + 17 y - 119 = 0$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: $( \pm 2,0 )$ ; major axis of length 18

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. $\theta = 45 ^ { \circ }$ , $( 10,10 )$

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

Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance) shown in the picture. d = 2.25 inches

Find the lengths of the major and minor axes of the ellipse graphed by following equation. $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 1 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1$

Convert the rectangular equation to polar form.Assume r > 1. $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 9 \left( x ^ { 2 } - y ^ { 2 } \right)$

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: y = -1

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 5 \cos \theta$

Find the standard form of the equation of the ellipse with the given characteristics. Foci: $( 0,0 ) , ( 6,0 )$ ; major axis of length 10.

Find the equation of the circle graphed below.

Find the center and vertices of the hyperbola. $12 x ^ { 2 } - 4 y ^ { 2 } - 72 x - 16 y + 44 = 0$

Find the center and foci of the ellipse. $\frac { ( x - 7 ) ^ { 2 } } { 55 } + \frac { ( y - 2 ) ^ { 2 } } { 64 } = 1$

Find the slope of the line with inclination $\Theta$ .Round your answer to four decimal places. $\Theta = 2.40 \text { radians }$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $3 y ^ { 2 } + 3 x ^ { 2 } - 21 x + 34 = 0$

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

Determine the angle θ\thetaθ through which the axes are rotated.Round your answer to two decimal places. 48x2+69xy+25y2=5048 x ^ { 2 } + 69 x y + 25 y ^ { 2 } = 5048x2+69xy+25y2=50

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 5).

Select the correct graph of the following equations of the hyperbola and find the center of hyperbola. (x−6)216−(y+2)21=1\frac { ( x - 6 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { 1 } = 116(x−6)2​−1(y+2)2​=1

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure). L = 5 inches Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 25x2+64y2−14x+17y−119=025 x ^ { 2 } + 64 y ^ { 2 } - 14 x + 17 y - 119 = 025x2+64y2−14x+17y−119=0

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: (±2,0)( \pm 2,0 )(±2,0) ; major axis of length 18

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

Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance) shown in the picture. d = 2.25 inches

Find the lengths of the major and minor axes of the ellipse graphed by following equation. (x′)21+(y′)236=1\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 1 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 11(x′)2​+36(y′)2​=1

Convert the rectangular equation to polar form.Assume r > 1. (x2+y2)2=9(x2−y2)\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 9 \left( x ^ { 2 } - y ^ { 2 } \right)(x2+y2)2=9(x2−y2)

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: y = -1

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=5cos⁡θr = 5 \cos \thetar=5cosθ

Find the standard form of the equation of the ellipse with the given characteristics. Foci: (0,0),(6,0)( 0,0 ) , ( 6,0 )(0,0),(6,0) ; major axis of length 10.

Find the equation of the circle graphed below.

Find the center and vertices of the hyperbola. 12x2−4y2−72x−16y+44=012 x ^ { 2 } - 4 y ^ { 2 } - 72 x - 16 y + 44 = 012x2−4y2−72x−16y+44=0

Find the center and foci of the ellipse. (x−7)255+(y−2)264=1\frac { ( x - 7 ) ^ { 2 } } { 55 } + \frac { ( y - 2 ) ^ { 2 } } { 64 } = 155(x−7)2​+64(y−2)2​=1

Find the slope of the line with inclination Θ\ThetaΘ .Round your answer to four decimal places. Θ=2.40 radians \Theta = 2.40 \text { radians }Θ=2.40 radians

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 3y2+3x2−21x+34=03 y ^ { 2 } + 3 x ^ { 2 } - 21 x + 34 = 03y2+3x2−21x+34=0

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

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $48 x ^ { 2 } + 69 x y + 25 y ^ { 2 } = 50$

Select the correct graph of the following equations of the hyperbola and find the center of hyperbola. $\frac { ( x - 6 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { 1 } = 1$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $25 x ^ { 2 } + 64 y ^ { 2 } - 14 x + 17 y - 119 = 0$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: $( \pm 2,0 )$ ; major axis of length 18

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

Find the lengths of the major and minor axes of the ellipse graphed by following equation. $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 1 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1$

Convert the rectangular equation to polar form.Assume r > 1. $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 9 \left( x ^ { 2 } - y ^ { 2 } \right)$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 5 \cos \theta$

Find the standard form of the equation of the ellipse with the given characteristics. Foci: $( 0,0 ) , ( 6,0 )$ ; major axis of length 10.

Find the center and vertices of the hyperbola. $12 x ^ { 2 } - 4 y ^ { 2 } - 72 x - 16 y + 44 = 0$

Find the center and foci of the ellipse. $\frac { ( x - 7 ) ^ { 2 } } { 55 } + \frac { ( y - 2 ) ^ { 2 } } { 64 } = 1$

Find the slope of the line with inclination $\Theta$ .Round your answer to four decimal places. $\Theta = 2.40 \text { radians }$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $3 y ^ { 2 } + 3 x ^ { 2 } - 21 x + 34 = 0$