Question 1

Select correct graph to graph rotated conic.  $r = \frac { 4 } { 2 + \sin ( \theta + \pi / 6 ) }$

Accepted Answer

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

Question 2

Use the Quadratic Formula to solve for $y$ .  $81 x ^ { 2 } - 90 x y + 25 y ^ { 2 } + 10 y = 0$

Accepted Answer

A)  $y = \frac { 90 x - 10 \pm \sqrt { ( 90 x - 10 ) ^ { 2 } + 8100 x ^ { 2 } } } { 50 }$ 
B)  $y = \frac { 90 x + 10 \pm \sqrt { ( 90 x + 10 ) ^ { 2 } + 8100 x ^ { 2 } } } { 50 }$ 
C)  $y = \frac { 90 x + 10 \pm \sqrt { ( 90 x - 10 ) ^ { 2 } - 8100 x ^ { 2 } } } { 50 }$ 
D)  $y = \frac { 90 x - 10 \pm \sqrt { ( 90 x - 10 ) ^ { 2 } - 8100 x ^ { 2 } } } { 50 }$ 
E)  $y = \frac { 90 x - 10 \pm \sqrt { ( 90 x + 10 ) ^ { 2 } - 8100 x ^ { 2 } } } { 50 }$ 
A)  $y = \frac { 90 x - 10 \pm \sqrt { ( 90 x - 10 ) ^ { 2 } + 8100 x ^ { 2 } } } { 50 }$ 
B)  $y = \frac { 90 x + 10 \pm \sqrt { ( 90 x + 10 ) ^ { 2 } + 8100 x ^ { 2 } } } { 50 }$ 
C)  $y = \frac { 90 x + 10 \pm \sqrt { ( 90 x - 10 ) ^ { 2 } - 8100 x ^ { 2 } } } { 50 }$ 
D)  $y = \frac { 90 x - 10 \pm \sqrt { ( 90 x - 10 ) ^ { 2 } - 8100 x ^ { 2 } } } { 50 }$ 
E)  $y = \frac { 90 x - 10 \pm \sqrt { ( 90 x + 10 ) ^ { 2 } - 8100 x ^ { 2 } } } { 50 }$

Question 3

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.  $2 x ^ { 2 } - y ^ { 2 } + 2 x + 5 y - 6 = 0$

Accepted Answer

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

Question 4

Convert the polar equation to rectangular form. $r = - 9 \sin \theta$

Accepted Answer

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

Question 5

Identify the conic.  $4 y ^ { 2 } - 3 x ^ { 2 } + 12 = 0$

Accepted Answer

A) Circle 
B) Ellipse 
C) Hyperbola 
D) Parabola 
E) Line 
A) Circle 
B) Ellipse 
C) Hyperbola 
D) Parabola 
E) Line

Question 6

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-7, -2) focus: (-5, -2)

Accepted Answer

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

Question 7

A solar oven uses a parabolic reflector to focus the sun's rays at a point 7 inches from the vertex of the reflector (see figure).   L = 7 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)  $y = 28 x ^ { 2 }$ 
B)  $y = \frac { 1 } { 7 } x ^ { 2 }$ 
C)  $x ^ { 2 } = 28 y$ 
D)  $y ^ { 2 } = 7 x$ 
E)  $x ^ { 2 } = 7 y$ 
A)  $y = 28 x ^ { 2 }$ 
B)  $y = \frac { 1 } { 7 } x ^ { 2 }$ 
C)  $x ^ { 2 } = 28 y$ 
D)  $y ^ { 2 } = 7 x$ 
E)  $x ^ { 2 } = 7 y$

Question 8

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.  $( 7.2 , - 3.0 )$

Accepted Answer

A) Rectangular coordinates: (-7.13,-1.02) 
B) Rectangular coordinates: (-1.02,-7.13) 
C) Rectangular coordinates: (-6.13,-1.02) 
D) Rectangular coordinates: (-7.13,-0.02) 
E) Rectangular coordinates: (-6.13,-0.02) 
A) Rectangular coordinates: (-7.13,-1.02) 
B) Rectangular coordinates: (-1.02,-7.13) 
C) Rectangular coordinates: (-6.13,-1.02) 
D) Rectangular coordinates: (-7.13,-0.02) 
E) Rectangular coordinates: (-6.13,-0.02)

Question 9

A moving conveyor is built so that it rises 9 meter for each 11 meters of horizontal travel.Find the inclination of the conveyor.Round your answers to one decimal place.

Accepted Answer

A)  $\Theta \approx 40.3 ^ { \circ }$ 
B)  $\Theta \approx 41.3 ^ { \circ }$ 
C)  $\Theta \approx 38.3 ^ { \circ }$ 
D)  $\Theta \approx 39.3 ^ { \circ }$ 
E)  $\Theta \approx 37.3 ^ { \circ }$ 
A)  $\Theta \approx 40.3 ^ { \circ }$ 
B)  $\Theta \approx 41.3 ^ { \circ }$ 
C)  $\Theta \approx 38.3 ^ { \circ }$ 
D)  $\Theta \approx 39.3 ^ { \circ }$ 
E)  $\Theta \approx 37.3 ^ { \circ }$

Question 10

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.  $$\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$$

Accepted Answer

A) Center: (0,0)Vertices: (-6,0)   
B) Center: (0,0)Vertices: (±6,0)  
C) Center: (0,0)Vertices: (-6,0)   
D) Center: (0,0)Vertices: (±6,0)   
E) Center: (0,0)Vertices: (6,0)   
A) Center: (0,0)Vertices: (-6,0)   
B) Center: (0,0)Vertices: (±6,0)  
C) Center: (0,0)Vertices: (-6,0)   
D) Center: (0,0)Vertices: (±6,0)   
E) Center: (0,0)Vertices: (6,0)

Question 11

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

Question 12

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( - 3,0 )$

Accepted Answer

A)  $x ^ { 2 } = y$ 
B)  $y ^ { 2 } = 12 x$ 
C)  $y ^ { 2 } = - 12 x$ 
D)  $x ^ { 2 } = 12 y$ 
E)  $x ^ { 2 } = - 12 y$ 
A)  $x ^ { 2 } = y$ 
B)  $y ^ { 2 } = 12 x$ 
C)  $y ^ { 2 } = - 12 x$ 
D)  $x ^ { 2 } = 12 y$ 
E)  $x ^ { 2 } = - 12 y$

Question 13

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

Accepted Answer

A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 7 \text { when } \theta = \frac { 3 \pi } { 2 }$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 7 \text { when } \theta = \frac { 3 \pi } { 2 }$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 7 \text { when } \theta = \frac { 3 \pi } { 2 }$    
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 7 \text { when } \theta = \frac { 3 \pi } { 2 }$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 7 \text { when } \theta = \frac { 3 \pi } { 2 }$   
A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 7 \text { when } \theta = \frac { 3 \pi } { 2 }$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 7 \text { when } \theta = \frac { 3 \pi } { 2 }$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 7 \text { when } \theta = \frac { 3 \pi } { 2 }$    
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 7 \text { when } \theta = \frac { 3 \pi } { 2 }$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 7 \text { when } \theta = \frac { 3 \pi } { 2 }$

Question 14

Consider the equation $r = 3 \sin k \varphi$ .Select the correct graph of the equation for $k = 1.5$ .

Accepted Answer

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

Question 15

Identify the conic and select its correct graph.  $r = \frac { 5 } { 5 + \sin \theta }$

Accepted Answer

A)  $e = \frac { 1 } { 5 } < 1 \Rightarrow$ Ellipse   
B)  $e = \frac { 1 } { 5 } < 1 \Rightarrow$ Ellipse   
C)  $e = \frac { 1 } { 5 } < 1 \Rightarrow$ Ellipse   
D)  $e = \frac { 1 } { 5 } < 1 \Rightarrow$ Ellipse   
E)  $e = \frac { 1 } { 5 } < 1 \Rightarrow$ Ellipse   
A)  $e = \frac { 1 } { 5 } < 1 \Rightarrow$ Ellipse   
B)  $e = \frac { 1 } { 5 } < 1 \Rightarrow$ Ellipse   
C)  $e = \frac { 1 } { 5 } < 1 \Rightarrow$ Ellipse   
D)  $e = \frac { 1 } { 5 } < 1 \Rightarrow$ Ellipse   
E)  $e = \frac { 1 } { 5 } < 1 \Rightarrow$ Ellipse

Question 16

Sketch the graph of the ellipse, using the lateral recta.$16 x ^ { 2 } + 4 y ^ { 2 } = 64$

Accepted Answer

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

Question 17

Find the vertices and asymptotes of the hyperbola. $25 y ^ { 2 } - 4 x ^ { 2 } = 100$

Accepted Answer

A) vertices: (±2,0), asymptote: $y = \pm \frac { 5 } { 2 } x$ 
B) vertices: (0,±2), asymptote: $y = \pm \frac { 2 } { 5 } x$ 
C) vertices: (±2,0), asymptote: $y = \pm \frac { 2 } { 5 } x$ 
D) vertices: (0,±2), asymptote: $y = \pm \frac { 5 } { 2 } x$ 
E) vertices: (±2,5), asymptote: $y = \pm \frac { 2 } { 5 } x$ 
A) vertices: (±2,0), asymptote: $y = \pm \frac { 5 } { 2 } x$ 
B) vertices: (0,±2), asymptote: $y = \pm \frac { 2 } { 5 } x$ 
C) vertices: (±2,0), asymptote: $y = \pm \frac { 2 } { 5 } x$ 
D) vertices: (0,±2), asymptote: $y = \pm \frac { 5 } { 2 } x$ 
E) vertices: (±2,5), asymptote: $y = \pm \frac { 2 } { 5 } x$

Question 18

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. 
Focus: (-4,0)

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 19

Select the curve represented by the parametric equations.(indicate the orientation of the curve)  $$x = t - 1$$ $$y = 4 t + 1$$

Accepted Answer

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

Question 20

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -2)

Accepted Answer

A) y2 = -8x 
B) x2 = -8y 
C) x2 = -2y 
D) y2 = -2x 
E) x2 = 2y 
A) y2 = -8x 
B) x2 = -8y 
C) x2 = -2y 
D) y2 = -2x 
E) x2 = 2y

Select correct graph to graph rotated conic. $r = \frac { 4 } { 2 + \sin ( \theta + \pi / 6 ) }$

Use the Quadratic Formula to solve for $y$ . $81 x ^ { 2 } - 90 x y + 25 y ^ { 2 } + 10 y = 0$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $2 x ^ { 2 } - y ^ { 2 } + 2 x + 5 y - 6 = 0$

Convert the polar equation to rectangular form. $r = - 9 \sin \theta$

Identify the conic. $4 y ^ { 2 } - 3 x ^ { 2 } + 12 = 0$

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-7, -2) focus: (-5, -2)

A solar oven uses a parabolic reflector to focus the sun's rays at a point 7 inches from the vertex of the reflector (see figure). L = 7 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.

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 7.2 , - 3.0 )$

A moving conveyor is built so that it rises 9 meter for each 11 meters of horizontal travel.Find the inclination of the conveyor.Round your answers to one decimal place.

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$

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

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( - 3,0 )$

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

Consider the equation $r = 3 \sin k \varphi$ .Select the correct graph of the equation for $k = 1.5$ .

Identify the conic and select its correct graph. $r = \frac { 5 } { 5 + \sin \theta }$

Sketch the graph of the ellipse, using the lateral recta. $16 x ^ { 2 } + 4 y ^ { 2 } = 64$

Find the vertices and asymptotes of the hyperbola. $25 y ^ { 2 } - 4 x ^ { 2 } = 100$

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: (-4,0)

Select the curve represented by the parametric equations.(indicate the orientation of the curve) $x = t - 1$ $y = 4 t + 1$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -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

Exam 10: Topics In Analytic Geometry

Select correct graph to graph rotated conic. r=42+sin⁡(θ+π/6)r = \frac { 4 } { 2 + \sin ( \theta + \pi / 6 ) }r=2+sin(θ+π/6)4​

Use the Quadratic Formula to solve for yyy . 81x2−90xy+25y2+10y=081 x ^ { 2 } - 90 x y + 25 y ^ { 2 } + 10 y = 081x2−90xy+25y2+10y=0

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 2x2−y2+2x+5y−6=02 x ^ { 2 } - y ^ { 2 } + 2 x + 5 y - 6 = 02x2−y2+2x+5y−6=0

Convert the polar equation to rectangular form. r=−9sin⁡θr = - 9 \sin \thetar=−9sinθ

Identify the conic. 4y2−3x2+12=04 y ^ { 2 } - 3 x ^ { 2 } + 12 = 04y2−3x2+12=0

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-7, -2) focus: (-5, -2)

A solar oven uses a parabolic reflector to focus the sun's rays at a point 7 inches from the vertex of the reflector (see figure). L = 7 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.

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. (7.2,−3.0)( 7.2 , - 3.0 )(7.2,−3.0)

A moving conveyor is built so that it rises 9 meter for each 11 meters of horizontal travel.Find the inclination of the conveyor.Round your answers to one decimal place.

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. x236+y29=1\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 136x2​+9y2​=1

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

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: (−3,0)( - 3,0 )(−3,0)

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

Consider the equation r=3sin⁡kφr = 3 \sin k \varphir=3sinkφ .Select the correct graph of the equation for k=1.5k = 1.5k=1.5 .

Identify the conic and select its correct graph. r=55+sin⁡θr = \frac { 5 } { 5 + \sin \theta }r=5+sinθ5​

Sketch the graph of the ellipse, using the lateral recta. 16x2+4y2=6416 x ^ { 2 } + 4 y ^ { 2 } = 6416x2+4y2=64

Find the vertices and asymptotes of the hyperbola. 25y2−4x2=10025 y ^ { 2 } - 4 x ^ { 2 } = 10025y2−4x2=100

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: (-4,0)

Select the curve represented by the parametric equations.(indicate the orientation of the curve) x=t−1x = t - 1x=t−1 y=4t+1y = 4 t + 1y=4t+1

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -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

Select correct graph to graph rotated conic. $r = \frac { 4 } { 2 + \sin ( \theta + \pi / 6 ) }$

Use the Quadratic Formula to solve for $y$ . $81 x ^ { 2 } - 90 x y + 25 y ^ { 2 } + 10 y = 0$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $2 x ^ { 2 } - y ^ { 2 } + 2 x + 5 y - 6 = 0$

Convert the polar equation to rectangular form. $r = - 9 \sin \theta$

Identify the conic. $4 y ^ { 2 } - 3 x ^ { 2 } + 12 = 0$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 7.2 , - 3.0 )$

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$

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

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( - 3,0 )$

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

Consider the equation $r = 3 \sin k \varphi$ .Select the correct graph of the equation for $k = 1.5$ .

Identify the conic and select its correct graph. $r = \frac { 5 } { 5 + \sin \theta }$

Sketch the graph of the ellipse, using the lateral recta. $16 x ^ { 2 } + 4 y ^ { 2 } = 64$

Find the vertices and asymptotes of the hyperbola. $25 y ^ { 2 } - 4 x ^ { 2 } = 100$

Select the curve represented by the parametric equations.(indicate the orientation of the curve) $x = t - 1$ $y = 4 t + 1$