Question 1

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

Accepted Answer

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

Question 2

Select the graph of the following equation. ​   ​

Accepted Answer

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

Question 3

Select the graph for following equation. ​   ​

Accepted Answer

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

Question 4

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

Accepted Answer

A) Symmetric with respect to   , polar axis, pole Circle with radius  
​   
B) Symmetric with respect to   , polar axis, pole Circle with radius  
​   
C) Symmetric with respect to   , polar axis, pole Circle with radius  
​   
D) Symmetric with respect to   , polar axis, pole Circle with radius  
​   
E) Symmetric with respect to   , polar axis, pole Circle with radius  
​   
A) Symmetric with respect to   , polar axis, pole Circle with radius  
​   
B) Symmetric with respect to   , polar axis, pole Circle with radius  
​   
C) Symmetric with respect to   , polar axis, pole Circle with radius  
​   
D) Symmetric with respect to   , polar axis, pole Circle with radius  
​   
E) Symmetric with respect to   , polar axis, pole Circle with radius  
​

Question 5

Select the graph of the equation. ​   ​

Accepted Answer

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

Question 6

Identify the conic and select its correct graph. ​   ​

Accepted Answer

A)    Ellipse ​  
​
​ 
B)    Ellipse ​   
C)    Ellipse ​   
D)    Ellipse ​  
​ 
E)    Ellipse ​   
A)    Ellipse ​  
​
​ 
B)    Ellipse ​   
C)    Ellipse ​   
D)    Ellipse ​  
​ 
E)    Ellipse ​

Question 7

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

Accepted Answer

A) Polar coordinates:   
B) Polar coordinates:   
C) Polar coordinates:   
D) Polar coordinates:   
E) Polar coordinates:   
A) Polar coordinates:   
B) Polar coordinates:   
C) Polar coordinates:   
D) Polar coordinates:   
E) Polar coordinates:

Question 8

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

Question 9

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. ​   ​

Accepted Answer

A) Rectangular coordinates: (1.83,-0.81) 
B) Rectangular coordinates: (1.83,1.83) 
C) Rectangular coordinates: (-0.81,0.81) 
D) Rectangular coordinates: (1.83,0.15) 
E) Rectangular coordinates: (1.83,0.81) 
A) Rectangular coordinates: (1.83,-0.81) 
B) Rectangular coordinates: (1.83,1.83) 
C) Rectangular coordinates: (-0.81,0.81) 
D) Rectangular coordinates: (1.83,0.15) 
E) Rectangular coordinates: (1.83,0.81)

Question 10

Use the discriminant to classify the graph. ​   ​

Accepted Answer

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

Question 11

Identify the conic and select its correct graph. ​   ​

Accepted Answer

A)    Hyperbola ​  
​ 
B)    Hyperbola ​   
C)    Hyperbola ​   
D)    Hyperbola   
E) ​   Hyperbola   
A)    Hyperbola ​  
​ 
B)    Hyperbola ​   
C)    Hyperbola ​   
D)    Hyperbola   
E) ​   Hyperbola

Question 12

Find the angle   (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. ​   ​   ​

Accepted Answer

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

Question 13

Find the standard form of the equation of the ellipse with the given characteristics. ​
Center:   ; a = 3b; Foci:   , where a - thr semimajor axis, b - semiminor axis.
​

Accepted Answer

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

Question 14

Find the center, vertices and foci of the hyperbola. ​   ​

Accepted Answer

A) Center: (0, 0) Vertices: (0, 0)
Foci:   
B) Center: (0, 0) Vertices:  
Foci:   
C) Center: (0, 0) Vertices:  
Foci:   
D) Center: (0, 0) Vertices:  
Foci:   
E) Center: (0, 0) Vertices:  
Foci:   
A) Center: (0, 0) Vertices: (0, 0)
Foci:   
B) Center: (0, 0) Vertices:  
Foci:   
C) Center: (0, 0) Vertices:  
Foci:   
D) Center: (0, 0) Vertices:  
Foci:   
E) Center: (0, 0) Vertices:  
Foci:

Question 15

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

Accepted Answer

A)    
B)    
C)    
D)    
E) none of these 
A)    
B)    
C)    
D)    
E) none of these

Question 16

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola. ​   ​

Accepted Answer

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

Question 17

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

Accepted Answer

A) Polar coordinates:   
B) Polar coordinates:   
C) Polar coordinates:   
D) Polar coordinates:   
E) Polar coordinates:   
A) Polar coordinates:   
B) Polar coordinates:   
C) Polar coordinates:   
D) Polar coordinates:   
E) Polar coordinates:

Question 18

Select the polar equation of the conic for ​e = 0.75 and identify the conic for the following equation. ​   ​

Accepted Answer

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

Question 19

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. ​   ​   ​

Accepted Answer

A) Rectangular coordinates: (6,6) 
B) Rectangular coordinates: (6,0) 
C) Rectangular coordinates: (0,6) 
D) Rectangular coordinates: (-6,0) 
E) Rectangular coordinates: (0,-6) 
A) Rectangular coordinates: (6,6) 
B) Rectangular coordinates: (6,0) 
C) Rectangular coordinates: (0,6) 
D) Rectangular coordinates: (-6,0) 
E) Rectangular coordinates: (0,-6)

Question 20

Select the correct graph of the polar equation.Find an interval for   for which the graph is traced only once. ​   ​

Accepted Answer

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

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

Select the graph of the following equation.

Select the graph for following equation.

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

Select the graph of the equation.

Identify the conic and select its correct graph.

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 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 rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.

Use the discriminant to classify the graph.

Identify the conic and select its correct graph.

Find the angle (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.

Find the standard form of the equation of the ellipse with the given characteristics. Center: ; a = 3b; Foci: , where a - thr semimajor axis, b - semiminor axis.

Find the center, vertices and foci of the hyperbola.

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

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola.

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

Select the polar equation of the conic for e = 0.75 and identify the conic for the following equation.

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.

Select the correct graph of the polar equation.Find an interval for for which the graph is traced only once.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

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Exam 6: Topics-In-Analytic-Geometry

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

Select the graph of the following equation. ​ ​

Select the graph for following equation. ​ ​

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

Select the graph of the equation. ​ ​

Identify the conic and select its correct graph. ​ ​

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 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 rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. ​ ​

Use the discriminant to classify the graph. ​ ​

Identify the conic and select its correct graph. ​ ​

Find the angle (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. ​ ​ ​

Find the standard form of the equation of the ellipse with the given characteristics. ​ Center: ; a = 3b; Foci: , where a - thr semimajor axis, b - semiminor axis. ​

Find the center, vertices and foci of the hyperbola. ​ ​

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

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola. ​ ​

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

Select the polar equation of the conic for ​e = 0.75 and identify the conic for the following equation. ​ ​

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. ​ ​ ​

Select the correct graph of the polar equation.Find an interval for for which the graph is traced only once. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

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

Select the graph of the following equation.

Select the graph for following equation.

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

Select the graph of the equation.

Identify the conic and select its correct graph.

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 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 rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.

Use the discriminant to classify the graph.

Identify the conic and select its correct graph.

Find the angle (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.

Find the standard form of the equation of the ellipse with the given characteristics. Center: ; a = 3b; Foci: , where a - thr semimajor axis, b - semiminor axis.

Find the center, vertices and foci of the hyperbola.

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

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola.

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

Select the polar equation of the conic for e = 0.75 and identify the conic for the following equation.

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.

Select the correct graph of the polar equation.Find an interval for for which the graph is traced only once.