Question 1

Write the equation of the ellipse that has its center at the origin, focus at (1, 0) and vertex at (9, 0). ​

Accepted Answer

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

Question 2

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 3

Convert the polar equation to rectangular form. ​   ​

Accepted Answer

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

Question 4

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 5

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 54 feet and a height at the center of 12 feet.Find an equation of the semielliptical arch. ​

Accepted Answer

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

Question 6

Find the equation of the parabola so that its graph matches the description. ​   ; lower half of parabola
​

Accepted Answer

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

Question 7

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 8

Identify 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 9

Select the correct graph of the polar equation.Describe your viewing window. ​   ​

Accepted Answer

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

Question 10

Convert the polar equation to rectangular form. ​   ​

Accepted Answer

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

Question 11

Consider the equation. ​   ​
Without calculating, explain how to rewrite the equation so that it does not have an   -term.
​

Accepted Answer

A) To rewrite the equation   so that it does not have an   -term, you can solve for   in terms of   by completing the square or using the Quadratic Formula. 
B) To rewrite the equation   so that it does not have an   -term, you can solve for   in terms of   by completing the square or using the Quadratic Formula. 
C) To rewrite the equation   so that it has an   -term, you can solve for     in terms of   by taking square root or using the Quadratic Formula. 
D) To rewrite the equation   so that it has an   -term, you can solve for   in terms of   by completing the square or using the Quadratic Formula. 
E) To rewrite the equation   so that it has an   -term, you can solve for   in terms of   by completing the square or using the Quadratic Formula. 
A) To rewrite the equation   so that it does not have an   -term, you can solve for   in terms of   by completing the square or using the Quadratic Formula. 
B) To rewrite the equation   so that it does not have an   -term, you can solve for   in terms of   by completing the square or using the Quadratic Formula. 
C) To rewrite the equation   so that it has an   -term, you can solve for     in terms of   by taking square root or using the Quadratic Formula. 
D) To rewrite the equation   so that it has an   -term, you can solve for   in terms of   by completing the square or using the Quadratic Formula. 
E) To rewrite the equation   so that it has an   -term, you can solve for   in terms of   by completing the square or using the Quadratic Formula.

Question 12

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, and the pole   ​   
B) Symmetric with respect to   , the polar axis, and the pole   ​   
C) Symmetric with respect to   , the polar axis, and the pole   ​   
D) Symmetric with respect to   , the polar axis, and the pole   ​   
E) Symmetric with respect to   , the polar axis, and the pole   ​   
A) Symmetric with respect to   , the polar axis, and the pole   ​   
B) Symmetric with respect to   , the polar axis, and the pole   ​   
C) Symmetric with respect to   , the polar axis, and the pole   ​   
D) Symmetric with respect to   , the polar axis, and the pole   ​   
E) Symmetric with respect to   , the polar axis, and the pole   ​

Question 13

Find the vertex, focus, and directrix of the parabola. ​   ​

Accepted Answer

A) Vertex:   ; Focus:   ; Directrix:   
B) Vertex:   ; Focus:   ; Directrix:   
C) Vertex:   ; Focus:   ; Directrix:   
D) Vertex:   ; Focus:   ; Directrix:   
E) Vertex:   ; Focus:   ; Directrix:   
A) Vertex:   ; Focus:   ; Directrix:   
B) Vertex:   ; Focus:   ; Directrix:   
C) Vertex:   ; Focus:   ; Directrix:   
D) Vertex:   ; Focus:   ; Directrix:   
E) Vertex:   ; Focus:   ; Directrix:

Question 14

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -5
​

Accepted Answer

A) y2 = 20x 
B) y2 = -5x 
C) x2 = -20y 
D) x2 = -5y 
E) x2 = 20y 
A) y2 = 20x 
B) y2 = -5x 
C) x2 = -20y 
D) x2 = -5y 
E) x2 = 20y

Question 15

Identify the graph of the following ellipse. ​   ​

Accepted Answer

A)    ​ 
B)    ​ 
C)    ​ 
A)    ​ 
B)    ​ 
C)    ​

Question 16

Find the vertex and focus of the parabola.

Accepted Answer

A) vertex: (-7 , 0) focus: (0, 0) 
B) vertex: (7, 0) focus: (0, 0) 
C) vertex: (0, 0) focus: (-7, 0) 
D) vertex: (0, 0) focus: (0, -7) 
E) vertex: (0, 0) focus: (0, 7) 
A) vertex: (-7 , 0) focus: (0, 0) 
B) vertex: (7, 0) focus: (0, 0) 
C) vertex: (0, 0) focus: (-7, 0) 
D) vertex: (0, 0) focus: (0, -7) 
E) vertex: (0, 0) focus: (0, 7)

Question 17

Find a set of parametric equations for the rectangular equation. ​     ​

Accepted Answer

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

Question 18

Give the coordinates of the circle's center and its 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 19

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

Question 20

Find the vertex and focus of the parabola.

Accepted Answer

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

Write the equation of the ellipse that has its center at the origin, focus at (1, 0) and vertex at (9, 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.

Convert the polar equation to rectangular form.

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.

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 54 feet and a height at the center of 12 feet.Find an equation of the semielliptical arch.

Find the equation of the parabola so that its graph matches the description. ; lower half of parabola

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

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

Select the correct graph of the polar equation.Describe your viewing window.

Convert the polar equation to rectangular form.

Consider the equation. Without calculating, explain how to rewrite the equation so that it does not have an -term.

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

Find the vertex, focus, and directrix of the parabola.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -5

Identify the graph of the following ellipse.

Find the vertex and focus of the parabola.

Find a set of parametric equations for the rectangular equation.

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

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

Find the vertex and focus of the parabola.

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 ellipse that has its center at the origin, focus at (1, 0) and vertex at (9, 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. ​ ​

Convert the polar equation to rectangular form. ​ ​

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. ​ ​

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 54 feet and a height at the center of 12 feet.Find an equation of the semielliptical arch. ​

Find the equation of the parabola so that its graph matches the description. ​ ; lower half of parabola ​

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

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

Select the correct graph of the polar equation.Describe your viewing window. ​ ​

Convert the polar equation to rectangular form. ​ ​

Consider the equation. ​ ​ Without calculating, explain how to rewrite the equation so that it does not have an -term. ​

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

Find the vertex, focus, and directrix of the parabola. ​ ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -5 ​

Identify the graph of the following ellipse. ​ ​

Find the vertex and focus of the parabola.

Find a set of parametric equations for the rectangular equation. ​ ​

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

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

Find the vertex and focus of the parabola.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Write the equation of the ellipse that has its center at the origin, focus at (1, 0) and vertex at (9, 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.

Convert the polar equation to rectangular form.

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.

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 54 feet and a height at the center of 12 feet.Find an equation of the semielliptical arch.

Find the equation of the parabola so that its graph matches the description. ; lower half of parabola

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

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

Select the correct graph of the polar equation.Describe your viewing window.

Convert the polar equation to rectangular form.

Consider the equation. Without calculating, explain how to rewrite the equation so that it does not have an -term.

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

Find the vertex, focus, and directrix of the parabola.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -5

Identify the graph of the following ellipse.

Find a set of parametric equations for the rectangular equation.

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

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