Question 1

Select the polar equation with graph. ​   ​

Accepted Answer

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

Question 2

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

Question 3

Identify the conic and select its correct graph. ​   ​

Accepted Answer

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

Question 4

Find the vertex and focus of the parabola.

Accepted Answer

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

Question 5

Select the graph of the equation. ​   ​

Accepted Answer

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

Question 6

Find the Eccentricity of the conic. ​   ​

Accepted Answer

A) Eccentricity:   
B) Eccentricity:   
C) Eccentricity:   
D) Eccentricity:   
E) Eccentricity:   
A) Eccentricity:   
B) Eccentricity:   
C) Eccentricity:   
D) Eccentricity:   
E) Eccentricity:

Question 7

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

Accepted Answer

A) Rectangular coordinates: (3.5,1.62) 
B) Rectangular coordinates: (4.50,0.83) 
C) Rectangular coordinates: (-0.17,3.50) 
D) Rectangular coordinates: (0.83,4.50) 
E) Rectangular coordinates: (3.50,-0.17) 
A) Rectangular coordinates: (3.5,1.62) 
B) Rectangular coordinates: (4.50,0.83) 
C) Rectangular coordinates: (-0.17,3.50) 
D) Rectangular coordinates: (0.83,4.50) 
E) Rectangular coordinates: (3.50,-0.17)

Question 8

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1) and the line as a function of m. ​

Accepted Answer

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

Question 9

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​   ​

Accepted Answer

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

Question 10

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Horizontal axis and passes through the point   ​

Accepted Answer

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

Question 11

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Vertical axis and passes through the point (-8,-8)
​

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).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.   L = 5 inches

Accepted Answer

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

Question 14

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​
Directrix: x = 3
​

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Using following result find a set of parametric equation of conic. ​
Circle:   ​
Circle: center:   ; radius: 8
​

Accepted Answer

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

Question 17

By using a graphing utility select the correct graph of the polar equation. ​   ​

Accepted Answer

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

Question 18

Select the graph for following equation. ​   ​

Accepted Answer

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

Question 19

Find the inclination   (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. ​   ​

Accepted Answer

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

Question 20

Find the equation of the parabola with vertex at (1, 5) and focus at (-5, 5). ​

Accepted Answer

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

Select the polar equation with graph.

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

Identify the conic and select its correct graph.

Find the vertex and focus of the parabola.

Select the graph of the equation.

Find the Eccentricity of the conic.

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

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1) and the line as a function of m.

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Vertical axis and passes through the point (-8,-8)

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

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).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. L = 5 inches

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: x = 3

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

Using following result find a set of parametric equation of conic. Circle: Circle: center: ; radius: 8

By using a graphing utility select the correct graph of the polar equation.

Select the graph for following equation.

Find the inclination (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.

Find the equation of the parabola with vertex at (1, 5) and focus at (-5, 5).

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Select the polar equation with graph. ​ ​

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

Identify the conic and select its correct graph. ​ ​

Find the vertex and focus of the parabola.

Select the graph of the equation. ​ ​

Find the Eccentricity of the conic. ​ ​

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

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1) and the line as a function of m. ​

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​ ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Horizontal axis and passes through the point ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Vertical axis and passes through the point (-8,-8) ​

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

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).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. L = 5 inches

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​ Directrix: x = 3 ​

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

Using following result find a set of parametric equation of conic. ​ Circle: ​ Circle: center: ; radius: 8 ​

By using a graphing utility select the correct graph of the polar equation. ​ ​

Select the graph for following equation. ​ ​

Find the inclination (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. ​ ​

Find the equation of the parabola with vertex at (1, 5) and focus at (-5, 5). ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Select the polar equation with graph.

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

Identify the conic and select its correct graph.

Select the graph of the equation.

Find the Eccentricity of the conic.

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

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1) and the line as a function of m.

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Vertical axis and passes through the point (-8,-8)

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: x = 3

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

Using following result find a set of parametric equation of conic. Circle: Circle: center: ; radius: 8

By using a graphing utility select the correct graph of the polar equation.

Select the graph for following equation.

Find the inclination (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.

Find the equation of the parabola with vertex at (1, 5) and focus at (-5, 5).