Question 1

Write the equation of the circle graphed below.Express the equation in standard form.
​

Accepted Answer

The answer of Write the equation of the circle graphed...

Question 2

Determine the angle   through which the axes are rotated.Round your answer to two decimal places. ​   ​

Accepted Answer

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

Question 3

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

Question 4

Select the curve represented by the parametric equations. ​     ​

Accepted Answer

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

Question 5

Using following result find a set of parametric equation of conic. ​
Hyperbola:   ​
Hyperbola: vertices:   ; foci:   ​

Accepted Answer

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

Question 6

Find the inclination   (in radians and degrees) of the line.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 7

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 the polar axis   ​   
B) Symmetric with respect to the polar axis ​  
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C) Symmetric with respect to the polar axis ​  
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D) Symmetric with respect to the polar axis ​  
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E) Symmetric with respect to the polar axis ​  
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A) Symmetric with respect to the polar axis   ​   
B) Symmetric with respect to the polar axis ​  
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C) Symmetric with respect to the polar axis ​  
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D) Symmetric with respect to the polar axis ​  
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E) Symmetric with respect to the polar axis ​  
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Question 8

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -9

Accepted Answer

A) x2 = -9y 
B) y2 = 36x 
C) x2 = -36y 
D) x2 = 36y 
E) y2 = -9x 
A) x2 = -9y 
B) y2 = 36x 
C) x2 = -36y 
D) x2 = 36y 
E) y2 = -9x

Question 9

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

Accepted Answer

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

Question 10

Find the distance between the point and the line.Round your answer to four decimal places.   ​

Accepted Answer

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

Question 11

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 20 feet and a height at the center of 4 feet.Select the arch of the tunnel on a rectangular coordinate system with the center of the road entering the tunnel at the origin.Identify the coordinates of the known points. ​

Accepted Answer

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

Question 12

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 13

Sketch the graph of the ellipse, using the lateral recta. ​   ​

Accepted Answer

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

Question 14

The Comet Borrelly has an elliptical orbit with an eccentricity of ​   .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun? ​

Accepted Answer

A)    Closest point to the sun is   1.096 astronomical unit. 
B)    Closest point to the sun is   1.096 astronomical unit. 
C)    Closest point to the sun is   1.096 astronomical unit. 
D)    Closest point to the sun is   1.096 astronomical unit. 
E)    Closest point to the sun is   1.096 astronomical unit. 
A)    Closest point to the sun is   1.096 astronomical unit. 
B)    Closest point to the sun is   1.096 astronomical unit. 
C)    Closest point to the sun is   1.096 astronomical unit. 
D)    Closest point to the sun is   1.096 astronomical unit. 
E)    Closest point to the sun is   1.096 astronomical unit.

Question 15

Find the vertex and focus of the parabola.   ​

Accepted Answer

A) vertex: (0,0) focus: (0,-2) 
B) vertex: (2,0) focus: (0,0) 
C) vertex: (0,0) focus: (-2,0) 
D) vertex: (0,0) focus: (0,2) 
E) vertex: (-2,0) focus: (0,0) 
A) vertex: (0,0) focus: (0,-2) 
B) vertex: (2,0) focus: (0,0) 
C) vertex: (0,0) focus: (-2,0) 
D) vertex: (0,0) focus: (0,2) 
E) vertex: (-2,0) focus: (0,0)

Question 16

Find a polar equation of the conic with its focus at the pole. ​
Conics
Eccentrity
Directrix
Parabola     ​
​

Accepted Answer

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

Question 17

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 18

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Accepted Answer

A)    , focus:   
B)    , focus:   
C)    , focus:   
D)    , focus: (0,-4) 
E)    , focus:   
A)    , focus:   
B)    , focus:   
C)    , focus:   
D)    , focus: (0,-4) 
E)    , focus:

Question 19

Identify the conic by writing the equation in standard form.

Accepted Answer

A)    ; hyperbola 
B)    ; hyperbola 
C)    ; hyperbola 
D)    ; ellipse 
E)    ; ellipse 
A)    ; hyperbola 
B)    ; hyperbola 
C)    ; hyperbola 
D)    ; ellipse 
E)    ; ellipse

Question 20

Find the center and vertices of the ellipse. ​   ​

Accepted Answer

A) center:   ; vertices:   
B) center:   ; vertices:   
C) center:   ; vertices:   
D) center:   ; vertices:   
E) center:   ; vertices:   
A) center:   ; vertices:   
B) center:   ; vertices:   
C) center:   ; vertices:   
D) center:   ; vertices:   
E) center:   ; vertices:

Write the equation of the circle graphed below.Express the equation in standard form.

Determine the angle through which the axes are rotated.Round your answer to two decimal places.

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.

Select the curve represented by the parametric equations.

Using following result find a set of parametric equation of conic. Hyperbola: Hyperbola: vertices: ; foci:

Find the inclination (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.

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

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -9

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

Find the distance between the point and the line.Round your answer to four decimal places.

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

Sketch the graph of the ellipse, using the lateral recta.

The Comet Borrelly has an elliptical orbit with an eccentricity of .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun?

Find the vertex and focus of the parabola.

Find a polar equation of the conic with its focus at the pole. Conics Eccentrity Directrix Parabola

Identify the conic and select its correct graph.

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Identify the conic by writing the equation in standard form.

Find the center and vertices of the ellipse.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Write the equation of the circle graphed below.Express the equation in standard form. ​

Determine the angle through which the axes are rotated.Round your answer to two decimal places. ​ ​

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.

Select the curve represented by the parametric equations. ​ ​

Using following result find a set of parametric equation of conic. ​ Hyperbola: ​ Hyperbola: vertices: ; foci: ​

Find the inclination (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​ ​

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

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -9

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

Find the distance between the point and the line.Round your answer to four decimal places. ​

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

Sketch the graph of the ellipse, using the lateral recta. ​ ​

The Comet Borrelly has an elliptical orbit with an eccentricity of ​ .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun? ​

Find the vertex and focus of the parabola. ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Eccentrity Directrix Parabola ​ ​

Identify the conic and select its correct graph. ​ ​

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Identify the conic by writing the equation in standard form.

Find the center and vertices of the ellipse. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Write the equation of the circle graphed below.Express the equation in standard form.

Determine the angle through which the axes are rotated.Round your answer to two decimal places.

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.

Select the curve represented by the parametric equations.

Using following result find a set of parametric equation of conic. Hyperbola: Hyperbola: vertices: ; foci:

Find the inclination (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.

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

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

Find the distance between the point and the line.Round your answer to four decimal places.

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

Sketch the graph of the ellipse, using the lateral recta.

The Comet Borrelly has an elliptical orbit with an eccentricity of .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun?

Find the vertex and focus of the parabola.

Find a polar equation of the conic with its focus at the pole. Conics Eccentrity Directrix Parabola

Identify the conic and select its correct graph.

Find the center and vertices of the ellipse.