Question 1

Graph the hyperbola. $4 x ^ { 2 } - 16 y ^ { 2 } = 64$

Accepted Answer

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

Question 2

Find the standard form of the equation of the ellipse with the given characteristics.
vertices: (-1, -11), (-1, 7), minor axis of length 2

Accepted Answer

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

Question 3

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.  $\begin{array} { l } 
x - 2 y = 9 \
10 x + 2 y = 7
\end{array}$

Accepted Answer

A)  $\Theta \approx 1.3045 \text { radians } \approx 75.7 ^ { \circ }$ 
B)  $\Theta \approx 1.3045 \text { radians } \approx 74.7 ^ { \circ }$ 
C)  $\Theta \approx 1.3045 \text { radians } \approx 73.7 ^ { \circ }$ 
D)  $\theta \approx 1.3045 \text { radians } \approx 76.7 ^ { \circ }$ 
E)  $\Theta \approx 1.3045 \text { radians } \approx 72.7 ^ { \circ }$ 
A)  $\Theta \approx 1.3045 \text { radians } \approx 75.7 ^ { \circ }$ 
B)  $\Theta \approx 1.3045 \text { radians } \approx 74.7 ^ { \circ }$ 
C)  $\Theta \approx 1.3045 \text { radians } \approx 73.7 ^ { \circ }$ 
D)  $\theta \approx 1.3045 \text { radians } \approx 76.7 ^ { \circ }$ 
E)  $\Theta \approx 1.3045 \text { radians } \approx 72.7 ^ { \circ }$

Question 4

Find the vertices and asymptotes of the hyperbola. $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 81 } = 1$

Accepted Answer

A) vertices: (0, ±8) asymptote: y = ± $\frac { 9 } { 8 }$ x 
B) vertices: (0, ±8) asymptote: y = ± $\frac { 8 } { 9 }$ x 
C) vertices: (±8, 0) asymptote: y = ± $\frac { 9 } { 8 }$ x 
D) vertices: (±8, 0) asymptote: y = ± $\frac { 8 } { 9 }$ x 
E) vertices: (±8, 9) asymptote: y = ± $\frac { 8 } { 9 }$ x 
A) vertices: (0, ±8) asymptote: y = ± $\frac { 9 } { 8 }$ x 
B) vertices: (0, ±8) asymptote: y = ± $\frac { 8 } { 9 }$ x 
C) vertices: (±8, 0) asymptote: y = ± $\frac { 9 } { 8 }$ x 
D) vertices: (±8, 0) asymptote: y = ± $\frac { 8 } { 9 }$ x 
E) vertices: (±8, 9) asymptote: y = ± $\frac { 8 } { 9 }$ x

Question 5

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.  $4 x ^ { 2 } + 3 y ^ { 2 } + 5 x - 28 y + 58 = 0$

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

Question 6

As a speeding train crosses a trestle over a deep gorge, a child drops his toy plane from the window.The path of the toy plane is modeled by $x ^ { 2 } = - 6.0 ( y - 110 )$ , where y is the height above the floor of the gorge and distances are measured in feet.How far will the toy plane travel horizontally before it hits the bottom of the gorge? [Note: The toy plane does not glide; it "drops like a rock."]

Accepted Answer

A) 6.0 ft 
B) 10 ft 
C) 25.7 ft 
D) 110 ft 
E) 660.0 ft 
A) 6.0 ft 
B) 10 ft 
C) 25.7 ft 
D) 110 ft 
E) 660.0 ft

Question 7

Select the graph of the equation.  $r = 2 \sec \left( \theta - \frac { \pi } { 4 } \right)$

Accepted Answer

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

Question 8

Convert the rectangular equation to polar form.Assume r > 1. $x = 15$

Accepted Answer

A)  $r = 15 \sec \theta$ 
B)  $r = \csc \theta$ 
C)  $r = 15 \sin \theta$ 
D)  $r = 15 \csc \theta$ 
E)  $r = 15 \cos \theta$ 
A)  $r = 15 \sec \theta$ 
B)  $r = \csc \theta$ 
C)  $r = 15 \sin \theta$ 
D)  $r = 15 \csc \theta$ 
E)  $r = 15 \cos \theta$

Question 9

Find the center and vertices of the hyperbola and select its graph, using asymptotes as sketching aids.  $4 y ^ { 2 } - 25 x ^ { 2 } = 100$

Accepted Answer

A) Centre: (0,0)Vertices: (0,-5)   
B) Centre: (0,0)Vertices: (±5,0)   
C) Centre: (0,0)Vertices: (0,±5)   
D) Centre: (0,0)Vertices: (0,5)   
E) Centre: (0,0)Vertices: (5,0)   
A) Centre: (0,0)Vertices: (0,-5)   
B) Centre: (0,0)Vertices: (±5,0)   
C) Centre: (0,0)Vertices: (0,±5)   
D) Centre: (0,0)Vertices: (0,5)   
E) Centre: (0,0)Vertices: (5,0)

Question 10

Find the inclination $\theta$ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.  $( 4,5 ) , ( 7,8 )$

Accepted Answer

A)  $\Theta \approx 0.7854 \text { radians } \approx 46.0 ^ { \circ }$ 
B)  $\Theta \approx 0.7854 \text { radians } \approx 44.0 ^ { \circ }$ 
C)  $\Theta \approx 0.7854 \text { radians } \approx 47.0 ^ { \circ }$ 
D)  $\Theta \approx 0.7854 \text { radians } \approx 43.0 ^ { \circ }$ 
E)  $\Theta \approx 0.7854 \text { radians } \approx 45.0 ^ { \circ }$ 
A)  $\Theta \approx 0.7854 \text { radians } \approx 46.0 ^ { \circ }$ 
B)  $\Theta \approx 0.7854 \text { radians } \approx 44.0 ^ { \circ }$ 
C)  $\Theta \approx 0.7854 \text { radians } \approx 47.0 ^ { \circ }$ 
D)  $\Theta \approx 0.7854 \text { radians } \approx 43.0 ^ { \circ }$ 
E)  $\Theta \approx 0.7854 \text { radians } \approx 45.0 ^ { \circ }$

Question 11

Select the correct equation of the following graph.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$ 
B)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 36 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 0$ 
E)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$ 
A)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$ 
B)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 36 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 0$ 
E)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$

Question 12

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.  $\begin{array} { l } 
x = | t - 1 | \
y = t + 5
\end{array}$

Accepted Answer

A)  $x = | y - 1 | \text { OR } y = x + 1 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
B)  $x = | y - 6 | \text { OR } y = x + 6 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
C)  $x = | y + 6 | \text { OR } y = x + 6 , x \geq 0 \text { and } y = x + 6 , x \geq 0$ 
D)  $x = | y - 5 | \text { OR } y = x + 5 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
E)  $x = | y + 5 | \text { OR } y = x - 1 , x \geq 0 \text { and } y = - x + 5 , x \geq 0$ 
A)  $x = | y - 1 | \text { OR } y = x + 1 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
B)  $x = | y - 6 | \text { OR } y = x + 6 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
C)  $x = | y + 6 | \text { OR } y = x + 6 , x \geq 0 \text { and } y = x + 6 , x \geq 0$ 
D)  $x = | y - 5 | \text { OR } y = x + 5 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
E)  $x = | y + 5 | \text { OR } y = x - 1 , x \geq 0 \text { and } y = - x + 5 , x \geq 0$

Question 13

Find the inclination $\theta$ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.  $( 12,9 ) , ( 4,3 )$

Accepted Answer

A)  $\Theta \approx 0.6435 \text { radians } \approx 36.9$ 
B)  $\Theta \approx 0.6435 \text { radians } \approx 37.9$ 
C)  $\Theta \approx 0.6435 \text { radians } \approx 35.9$ 
D)  $\Theta \approx 0.6435 \text { radians } \approx 38.9$ 
E)  $\Theta \approx 0.6435 \text { radians } \approx 34.9$ 
A)  $\Theta \approx 0.6435 \text { radians } \approx 36.9$ 
B)  $\Theta \approx 0.6435 \text { radians } \approx 37.9$ 
C)  $\Theta \approx 0.6435 \text { radians } \approx 35.9$ 
D)  $\Theta \approx 0.6435 \text { radians } \approx 38.9$ 
E)  $\Theta \approx 0.6435 \text { radians } \approx 34.9$

Question 14

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r ^ { 2 } = 4 \cos 2 \theta$

Accepted Answer

A) Symmetric with respectto the polar axis, $\theta = \frac { \pi } { 2 }$ , and the poleLemniscate   
B) Symmetric with respectto the polar axis, $\theta = \frac { \pi } { 2 }$ , and the poleLemniscate   
C) Symmetric with respectto the polar axis, $\theta = \frac { \pi } { 2 }$ , and the poleLemniscate   
D) Symmetric with respectto the polar axis, $\theta = \frac { \pi } { 2 }$ , and the poleLemniscate   
E) Symmetric with respectto the polar axis, $\theta = \frac { \pi } { 2 }$ , and the poleLemniscate   
A) Symmetric with respectto the polar axis, $\theta = \frac { \pi } { 2 }$ , and the poleLemniscate   
B) Symmetric with respectto the polar axis, $\theta = \frac { \pi } { 2 }$ , and the poleLemniscate   
C) Symmetric with respectto the polar axis, $\theta = \frac { \pi } { 2 }$ , and the poleLemniscate   
D) Symmetric with respectto the polar axis, $\theta = \frac { \pi } { 2 }$ , and the poleLemniscate   
E) Symmetric with respectto the polar axis, $\theta = \frac { \pi } { 2 }$ , and the poleLemniscate

Question 15

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = 2$

Accepted Answer

A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 2$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 2$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 2$   
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 2$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 2$    
A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 2$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 2$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 2$   
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 2$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 2$

Question 16

Find the distance between the point and the line.Round your answer to four decimal places. Point Line
$$( 2,4 ) \quad 5 x - y = 10$$

Accepted Answer

A)  $d \approx 2.7889$ 
B)  $d \approx 1.7889$ 
C)  $d \approx 3.7889$ 
D)  $d \approx 0.7889$ 
E)  $d \approx 4.7889$ 
A)  $d \approx 2.7889$ 
B)  $d \approx 1.7889$ 
C)  $d \approx 3.7889$ 
D)  $d \approx 0.7889$ 
E)  $d \approx 4.7889$

Question 17

Write the equation of the ellipse with foci at (2, 2), (6, 2), and b = 4, where b - semiminor axis.

Accepted Answer

A)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } - \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = - 1$ 
D)  $\frac { ( x + 4 ) ^ { 2 } } { 20 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ 
E)  $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 20 } = 1$ 
A)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } - \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = - 1$ 
D)  $\frac { ( x + 4 ) ^ { 2 } } { 20 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ 
E)  $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 20 } = 1$

Question 18

Find the center and the vertices of the ellipse. $81 x ^ { 2 } + y ^ { 2 } = 81$

Accepted Answer

A) center: (-9, 9); vertices: (-1, -9), (1, 9) 
B) center: (0, 0); vertices: (0, -9), (0, 9) 
C) center: (0, 0); vertices: (-9, -1), (9, 1) 
D) center: (0, 0); vertices: (-9, 0), (9, 0) 
E) center: (-9, 9); vertices: (-1, 0), (1, 0) 
A) center: (-9, 9); vertices: (-1, -9), (1, 9) 
B) center: (0, 0); vertices: (0, -9), (0, 9) 
C) center: (0, 0); vertices: (-9, -1), (9, 1) 
D) center: (0, 0); vertices: (-9, 0), (9, 0) 
E) center: (-9, 9); vertices: (-1, 0), (1, 0)

Question 19

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.  $x ^ { 2 } + y ^ { 2 } - 9 x + 3 y - 16 = 0$

Accepted Answer

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

Question 20

Find the inclination  (in degrees) of the line with a slope of m.Round your answer to one decimal places.  $m = - 1.5$

Accepted Answer

A)  $\Theta \approx 124.7 ^ { \circ }$ 
B)  $\Theta \approx 125.7 ^ { \circ }$ 
C)  $\Theta \approx 123.7 ^ { \circ }$ 
D)  $\Theta \approx 121.7 ^ { \circ }$ 
E)  $\Theta \approx 122.7 ^ { \circ }$ 
A)  $\Theta \approx 124.7 ^ { \circ }$ 
B)  $\Theta \approx 125.7 ^ { \circ }$ 
C)  $\Theta \approx 123.7 ^ { \circ }$ 
D)  $\Theta \approx 121.7 ^ { \circ }$ 
E)  $\Theta \approx 122.7 ^ { \circ }$

Graph the hyperbola. $4 x ^ { 2 } - 16 y ^ { 2 } = 64$

Find the standard form of the equation of the ellipse with the given characteristics. vertices: (-1, -11), (-1, 7), minor axis of length 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. x-2y=9 10x+2y=7

Find the vertices and asymptotes of the hyperbola. $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 81 } = 1$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $4 x ^ { 2 } + 3 y ^ { 2 } + 5 x - 28 y + 58 = 0$

Select the graph of the equation. $r = 2 \sec \left( \theta - \frac { \pi } { 4 } \right)$

Convert the rectangular equation to polar form.Assume r > 1. $x = 15$

Find the center and vertices of the hyperbola and select its graph, using asymptotes as sketching aids. $4 y ^ { 2 } - 25 x ^ { 2 } = 100$

Find the inclination $\theta$ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $( 4,5 ) , ( 7,8 )$

Select the correct equation of the following graph.

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=|t-1| y=t+5

Find the inclination $\theta$ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $( 12,9 ) , ( 4,3 )$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r ^ { 2 } = 4 \cos 2 \theta$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 2,4 ) \quad 5 x - y = 10$

Write the equation of the ellipse with foci at (2, 2), (6, 2), and b = 4, where b - semiminor axis.

Find the center and the vertices of the ellipse. $81 x ^ { 2 } + y ^ { 2 } = 81$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $x ^ { 2 } + y ^ { 2 } - 9 x + 3 y - 16 = 0$

Find the inclination (in degrees) of the line with a slope of m.Round your answer to one decimal places. $m = - 1.5$

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

Graph the hyperbola. 4x2−16y2=644 x ^ { 2 } - 16 y ^ { 2 } = 644x2−16y2=64

Find the standard form of the equation of the ellipse with the given characteristics. vertices: (-1, -11), (-1, 7), minor axis of length 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. x-2y=9 10x+2y=7

Find the vertices and asymptotes of the hyperbola. x264−y281=1\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 81 } = 164x2​−81y2​=1

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 4x2+3y2+5x−28y+58=04 x ^ { 2 } + 3 y ^ { 2 } + 5 x - 28 y + 58 = 04x2+3y2+5x−28y+58=0

Select the graph of the equation. r=2sec⁡(θ−π4)r = 2 \sec \left( \theta - \frac { \pi } { 4 } \right)r=2sec(θ−4π​)

Convert the rectangular equation to polar form.Assume r > 1. x=15x = 15x=15

Find the center and vertices of the hyperbola and select its graph, using asymptotes as sketching aids. 4y2−25x2=1004 y ^ { 2 } - 25 x ^ { 2 } = 1004y2−25x2=100

Find the inclination θ\thetaθ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. (4,5),(7,8)( 4,5 ) , ( 7,8 )(4,5),(7,8)

Select the correct equation of the following graph.

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=|t-1| y=t+5

Find the inclination θ\thetaθ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. (12,9),(4,3)( 12,9 ) , ( 4,3 )(12,9),(4,3)

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r2=4cos⁡2θr ^ { 2 } = 4 \cos 2 \thetar2=4cos2θ

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=2r = 2r=2

Find the distance between the point and the line.Round your answer to four decimal places. Point Line (2,4)5x−y=10( 2,4 ) \quad 5 x - y = 10(2,4)5x−y=10

Write the equation of the ellipse with foci at (2, 2), (6, 2), and b = 4, where b - semiminor axis.

Find the center and the vertices of the ellipse. 81x2+y2=8181 x ^ { 2 } + y ^ { 2 } = 8181x2+y2=81

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. x2+y2−9x+3y−16=0x ^ { 2 } + y ^ { 2 } - 9 x + 3 y - 16 = 0x2+y2−9x+3y−16=0

Find the inclination (in degrees) of the line with a slope of m.Round your answer to one decimal places. m=−1.5m = - 1.5m=−1.5

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

Graph the hyperbola. $4 x ^ { 2 } - 16 y ^ { 2 } = 64$

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-2y=9 10x+2y=7

Find the vertices and asymptotes of the hyperbola. $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 81 } = 1$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $4 x ^ { 2 } + 3 y ^ { 2 } + 5 x - 28 y + 58 = 0$

Select the graph of the equation. $r = 2 \sec \left( \theta - \frac { \pi } { 4 } \right)$

Convert the rectangular equation to polar form.Assume r > 1. $x = 15$

Find the center and vertices of the hyperbola and select its graph, using asymptotes as sketching aids. $4 y ^ { 2 } - 25 x ^ { 2 } = 100$

Find the inclination $\theta$ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $( 4,5 ) , ( 7,8 )$

Find the inclination $\theta$ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $( 12,9 ) , ( 4,3 )$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r ^ { 2 } = 4 \cos 2 \theta$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 2,4 ) \quad 5 x - y = 10$

Find the center and the vertices of the ellipse. $81 x ^ { 2 } + y ^ { 2 } = 81$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $x ^ { 2 } + y ^ { 2 } - 9 x + 3 y - 16 = 0$

Find the inclination (in degrees) of the line with a slope of m.Round your answer to one decimal places. $m = - 1.5$