Question 1

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Foci:   ; major axis of length 18
​

Accepted Answer

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

Question 2

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 3

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 4

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

Accepted Answer

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

Question 5

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) ​

Question 6

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

Accepted Answer

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

Question 7

Identify the conic as a circle or an ellipse then find the radius for circle or center for ellipse. ​   ​

Accepted Answer

A) Ellipse Center:   
B) Ellipse Center: 1 
C) Circle Radius: 1 
D) Circle Radius:   
E) None of the above 
A) Ellipse Center:   
B) Ellipse Center: 1 
C) Circle Radius: 1 
D) Circle Radius:   
E) None of the above

Question 8

Give the standard form of the equation of the parabola with the given characteristics. vertex: (7, 8) focus: (5, 8)

Accepted Answer

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

Question 9

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 10

Consider a line with slope m and y-intercept (0,3).Find the slope that yields the maximum distance between the point (2,1) and the line. ​

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

Consider the equation. ​   ​
Explain how to identify the graph of the equation.
​

Accepted Answer

A) Find the discriminant of the equation to identify the graph of the equation. 
B) Find the foci of the equation to identify the graph of the equation. 
C) Find the major axis of the equation to identify the graph of the equation. 
D) Find the minor axis of the equation to identify the graph of the equation. 
E) Find the vertices of the equation to identify the graph of the equation. 
A) Find the discriminant of the equation to identify the graph of the equation. 
B) Find the foci of the equation to identify the graph of the equation. 
C) Find the major axis of the equation to identify the graph of the equation. 
D) Find the minor axis of the equation to identify the graph of the equation. 
E) Find the vertices of the equation to identify the graph of the equation.

Question 13

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. ​   ​

Accepted Answer

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

Question 14

Identify the conic as a circle or an ellipse then find the center. ​   ​

Accepted Answer

A) Circle Center: (0,0) 
B) Ellipse Center: (0,0) 
C) ​Circle Center: (3,2) 
D) ​Ellipse Center: (3,2) 
E) ​Circle Center: (2,3) 
A) Circle Center: (0,0) 
B) Ellipse Center: (0,0) 
C) ​Circle Center: (3,2) 
D) ​Ellipse Center: (3,2) 
E) ​Circle Center: (2,3)

Question 15

Find the center and vertices of the ellipse. ​   ​

Accepted Answer

A) center: (9, 6) vertices: (-9, -6), (9, 6) 
B) center: (0, 0) vertices: (0, -9), (0, 9) 
C) center: (9, 0) vertices: (0, -6), (0, 6) 
D) center: (0, 0) vertices: (-6, 0), (6, 0) 
E) center: (0, 0) vertices: (-9, 0), (9, 0) 
A) center: (9, 6) vertices: (-9, -6), (9, 6) 
B) center: (0, 0) vertices: (0, -9), (0, 9) 
C) center: (9, 0) vertices: (0, -6), (0, 6) 
D) center: (0, 0) vertices: (-6, 0), (6, 0) 
E) center: (0, 0) vertices: (-9, 0), (9, 0)

Question 16

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​
A = (0,0), B = (3,6), C = (6,0)
​

Accepted Answer

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

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 graph for following equation. ​   ​

Accepted Answer

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

Question 19

Select the curve represented by the parametric equations. ​
Prolate cycloid:   ​

Accepted Answer

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

Question 20

Find the vertex and focus of the parabola from the given equation and select its graph. ​   ​

Accepted Answer

A) Vertex: (0,0) Focus: (-   ,0)   
B) Vertex: (0,0) Focus: (0,-   )   
C) Vertex: (0,0) Focus: (   ,0)   
D) Vertex: (0,0) Focus: (0,   )   
E) Vertex: (0,0) Focus: (   ,0)   
A) Vertex: (0,0) Focus: (-   ,0)   
B) Vertex: (0,0) Focus: (0,-   )   
C) Vertex: (0,0) Focus: (   ,0)   
D) Vertex: (0,0) Focus: (0,   )   
E) Vertex: (0,0) Focus: (   ,0)

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: ; major axis of length 18

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

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.

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

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

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

Identify the conic as a circle or an ellipse then find the radius for circle or center for ellipse.

Give the standard form of the equation of the parabola with the given characteristics. vertex: (7, 8) focus: (5, 8)

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

Consider a line with slope m and y-intercept (0,3).Find the slope that yields the maximum distance between the point (2,1) and the line.

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

Consider the equation. Explain how to identify the graph of the equation.

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form.

Identify the conic as a circle or an ellipse then find the center.

Find the center and vertices of the ellipse.

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. A = (0,0), B = (3,6), C = (6,0)

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

Select the graph for following equation.

Select the curve represented by the parametric equations. Prolate cycloid:

Find the vertex and focus of the parabola from the given equation and select its graph.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Foci: ; major axis of length 18 ​

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

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. ​ ​

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

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

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

Identify the conic as a circle or an ellipse then find the radius for circle or center for ellipse. ​ ​

Give the standard form of the equation of the parabola with the given characteristics. vertex: (7, 8) focus: (5, 8)

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

Consider a line with slope m and y-intercept (0,3).Find the slope that yields the maximum distance between the point (2,1) and the line. ​

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

Consider the equation. ​ ​ Explain how to identify the graph of the equation. ​

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. ​ ​

Identify the conic as a circle or an ellipse then find the center. ​ ​

Find the center and vertices of the ellipse. ​ ​

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​ A = (0,0), B = (3,6), C = (6,0) ​

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

Select the graph for following equation. ​ ​

Select the curve represented by the parametric equations. ​ Prolate cycloid: ​

Find the vertex and focus of the parabola from the given equation and select its graph. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: ; major axis of length 18

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

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.

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

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

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

Identify the conic as a circle or an ellipse then find the radius for circle or center for ellipse.

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

Consider a line with slope m and y-intercept (0,3).Find the slope that yields the maximum distance between the point (2,1) and the line.

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

Consider the equation. Explain how to identify the graph of the equation.

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form.

Identify the conic as a circle or an ellipse then find the center.

Find the center and vertices of the ellipse.

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. A = (0,0), B = (3,6), C = (6,0)

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

Select the graph for following equation.

Select the curve represented by the parametric equations. Prolate cycloid:

Find the vertex and focus of the parabola from the given equation and select its graph.