Question 1

Find a polar equation of the conic with its focus at the pole. ​
Conics
Vertex or vertices
Parabola   ​

Accepted Answer

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B)    
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D)    
E)    
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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

Convert the polar equation to rectangular form. ​   ​

Accepted Answer

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D)    
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D)    
E)

Question 4

Find the standard form of the equation of the ellipse with the given characteristics. ​
Foci:   ; major axis of length 12.
​

Accepted Answer

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B)    
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E)    
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E)

Question 5

An elliptical stained-glass insert is to be fitted in a 6ft by 4 ft rectangular opening (see figure).Using the coordinate system shown, find an equation for the ellipse. ​   ​

Accepted Answer

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

Question 6

Find the standard form of the equation of the ellipse with the following characteristics. focies: (±8,0) major axis of length: 22

Accepted Answer

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

Question 7

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. ​     ​

Accepted Answer

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

Question 8

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. ​   ​

Accepted Answer

A) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
B) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
C) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
D) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​
​   
E) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
A) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
B) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
C) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
D) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​
​   
E) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​

Question 9

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 6).Express the equation in standard form.

Accepted Answer

The answer of Find the equation of the parabola with...

Question 10

Convert the rectangular equation to polar form.Assume r > 1. ​   ​

Accepted Answer

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

Question 11

Find the center and vertices of the ellipse. ​   ​

Accepted Answer

A) center: (8, 6) vertices: (-8, -6), (8, 6) 
B) center: (0, 0) vertices: (0, -8), (0, 8) 
C) center: (0, 0) vertices: (-8, 0), (8, 0) 
D) center: (8, 0) vertices: (0, -6), (0, 6) 
E) center: (0, 0) vertices: (-6, 0), (6, 0) 
A) center: (8, 6) vertices: (-8, -6), (8, 6) 
B) center: (0, 0) vertices: (0, -8), (0, 8) 
C) center: (0, 0) vertices: (-8, 0), (8, 0) 
D) center: (8, 0) vertices: (0, -6), (0, 6) 
E) center: (0, 0) vertices: (-6, 0), (6, 0)

Question 12

Give the coordinates of the circle's center and it radius.
​   ​
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 13

Select the graph of the following equation: ​
​

Accepted Answer

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

Question 14

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. ​   ​

Accepted Answer

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

Question 15

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

Accepted Answer

A) Rectangular coordinates: (-3.97,5.09) 
B) Rectangular coordinates: (-2.97,5.09) 
C) Rectangular coordinates: (-3.97,4.09) 
D) Rectangular coordinates: (-2.97,4.09) 
E) Rectangular coordinates: (4.09,-3.97) 
A) Rectangular coordinates: (-3.97,5.09) 
B) Rectangular coordinates: (-2.97,5.09) 
C) Rectangular coordinates: (-3.97,4.09) 
D) Rectangular coordinates: (-2.97,4.09) 
E) Rectangular coordinates: (4.09,-3.97)

Question 16

Find the lengths of the major and minor axes of the ellipse graphed by following equation. ​   ​

Accepted Answer

A) Length of major axis is   Length of minor axis is   
B) Length of major axis is   Length of minor axis is   
C) Length of major axis is   Length of minor axis is   
D) Length of major axis is   Length of minor axis is   
E) None of the above 
A) Length of major axis is   Length of minor axis is   
B) Length of major axis is   Length of minor axis is   
C) Length of major axis is   Length of minor axis is   
D) Length of major axis is   Length of minor axis is   
E) None of the above

Question 17

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 18

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 19

Find the standard form of the equation of the ellipse with the given characteristics. ​
Foci:   , endpoints of the major axis:   ​

Accepted Answer

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

Question 20

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Foci:   ; asymptotes:   ​

Accepted Answer

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

Find a polar equation of the conic with its focus at the pole. Conics Vertex or vertices Parabola

Select the graph of the following equation.

Convert the polar equation to rectangular form.

Find the standard form of the equation of the ellipse with the given characteristics. Foci: ; major axis of length 12.

An elliptical stained-glass insert is to be fitted in a 6ft by 4 ft rectangular opening (see figure).Using the coordinate system shown, find an equation for the ellipse.

Find the standard form of the equation of the ellipse with the following characteristics. focies: (±8,0) major axis of length: 22

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 6).Express the equation in standard form.

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

Find the center and vertices of the ellipse.

Give the coordinates of the circle's center and it radius. Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

Select the graph of the following equation:

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

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

Find the lengths of the major and minor axes of the ellipse graphed by following equation.

Identify the conic and select its correct graph.

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

Find the standard form of the equation of the ellipse with the given characteristics. Foci: , endpoints of the major axis:

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Foci: ; asymptotes:

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Find a polar equation of the conic with its focus at the pole. ​ Conics Vertex or vertices Parabola ​

Select the graph of the following equation. ​ ​

Convert the polar equation to rectangular form. ​ ​

Find the standard form of the equation of the ellipse with the given characteristics. ​ Foci: ; major axis of length 12. ​

An elliptical stained-glass insert is to be fitted in a 6ft by 4 ft rectangular opening (see figure).Using the coordinate system shown, find an equation for the ellipse. ​ ​

Find the standard form of the equation of the ellipse with the following characteristics. focies: (±8,0) major axis of length: 22

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. ​ ​

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. ​ ​

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 6).Express the equation in standard form.

Convert the rectangular equation to polar form.Assume r > 1. ​ ​

Find the center and vertices of the ellipse. ​ ​

Give the coordinates of the circle's center and it radius. ​ ​ Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

Select the graph of the following equation: ​ ​

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. ​ ​

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

Find the lengths of the major and minor axes of the ellipse graphed by following equation. ​ ​

Identify the conic and select its correct graph. ​ ​

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

Find the standard form of the equation of the ellipse with the given characteristics. ​ Foci: , endpoints of the major axis: ​

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​ Foci: ; asymptotes: ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Find a polar equation of the conic with its focus at the pole. Conics Vertex or vertices Parabola

Select the graph of the following equation.

Convert the polar equation to rectangular form.

Find the standard form of the equation of the ellipse with the given characteristics. Foci: ; major axis of length 12.

An elliptical stained-glass insert is to be fitted in a 6ft by 4 ft rectangular opening (see figure).Using the coordinate system shown, find an equation for the ellipse.

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.

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

Find the center and vertices of the ellipse.

Give the coordinates of the circle's center and it radius. Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

Select the graph of the following equation:

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

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

Find the lengths of the major and minor axes of the ellipse graphed by following equation.

Identify the conic and select its correct graph.

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

Find the standard form of the equation of the ellipse with the given characteristics. Foci: , endpoints of the major axis:

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Foci: ; asymptotes: