Question 1

Select the parametric equations matching with the following graph. ​   ​

Accepted Answer

A) Serpentine curve:   
B) Serpentine curve:   
C) Serpentine curve:   
D) Serpentine curve:   
E) Serpentine curve:   
A) Serpentine curve:   
B) Serpentine curve:   
C) Serpentine curve:   
D) Serpentine curve:   
E) Serpentine curve:

Question 2

Using following result find a set of parametric equation of the line. ​   ​
Line: passes through (0,0) and   ​

Accepted Answer

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

Question 3

Find the standard form of the equation of the parabola with the given characteristics. ​
Vertex:   ; directrix:   ​

Accepted Answer

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

Question 4

Select the curve represented by the parametric equations. ​
Cycloid:   ​

Accepted Answer

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

Question 5

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus:

Accepted Answer

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

Question 6

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​
A = (0,0), B = (3,4), C = (4,-3)
​

Accepted Answer

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

Question 7

The   -coordinate system has been rotated   degrees from the   -coordinate system.The coordinates of a point in the   -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ​   ,   ​

Accepted Answer

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

Question 8

Identify the conic by writing the equation in standard form. ​   ​

Accepted Answer

A) ​   ; ellipse 
B) ​   ; ellipse 
C) ​   ; ellipse 
D) ​   ; ellipse 
E) ​   ; circle 
A) ​   ; ellipse 
B) ​   ; ellipse 
C) ​   ; ellipse 
D) ​   ; ellipse 
E) ​   ; circle

Question 9

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. ​   ​

Accepted Answer

A) Center: (0,0) Vertices: (±3,0)   
B) Center: (0,0) Vertices: (-3,0)   
C) Center: (0,0) Vertices: (3,0)
​   
D) Center: (0,0) Vertices: (±3,0)
​   
E) Center: (0,0) Vertices: (-3,0)
​   
A) Center: (0,0) Vertices: (±3,0)   
B) Center: (0,0) Vertices: (-3,0)   
C) Center: (0,0) Vertices: (3,0)
​   
D) Center: (0,0) Vertices: (±3,0)
​   
E) Center: (0,0) Vertices: (-3,0)
​

Question 10

As a speeding train crosses a trestle over a deep gorge, a child drops his toy plane from the window.The path of the toy plane is modeled by   , where y is the height above the floor of the gorge and distances are measured in feet.How far will the toy plane travel horizontally before it hits the bottom of the gorge? [Note: The toy plane does not glide; it "drops like a rock."]

Accepted Answer

A) 6.0 ft 
B) 10 ft 
C) 25.7 ft 
D) 110 ft 
E) 660.0 ft 
A) 6.0 ft 
B) 10 ft 
C) 25.7 ft 
D) 110 ft 
E) 660.0 ft

Question 11

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 12

Select the graph of   over the interval.Describe the part of the graph obtained in this case. ​   ​

Accepted Answer

A) ​   Lower half of circle 
B) ​   Lower half of circle 
C) ​   Lower half of circle 
D) ​   Lower half of circle 
E) ​   Lower half of circle 
A) ​   Lower half of circle 
B) ​   Lower half of circle 
C) ​   Lower half of circle 
D) ​   Lower half of circle 
E) ​   Lower half of circle

Question 13

The   -coordinate system has been rotated   degrees from the   -coordinate system.The coordinates of a point in the   -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ​   ,   ​

Accepted Answer

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

Question 14

Select the graph of the equation. ​   ​

Accepted Answer

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

Question 15

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. ​
Earth   miles   ​

Accepted Answer

A)    Perihelion distance:  
Aphelion distance:   
B)    Perihelion distance:  
Aphelion distance:   
C)    Perihelion distance:  
Aphelion distance:   
D)    Perihelion distance:  
Aphelion distance:   
E)    Perihelion distance:  
Aphelion distance:   
A)    Perihelion distance:  
Aphelion distance:   
B)    Perihelion distance:  
Aphelion distance:   
C)    Perihelion distance:  
Aphelion distance:   
D)    Perihelion distance:  
Aphelion distance:   
E)    Perihelion distance:  
Aphelion distance:

Question 16

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​
A = (-4,-5), B = (2,7), C = (5,7)
​

Accepted Answer

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

Question 17

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 18

Find the standard form of the equation of the ellipse with the following graph.

Accepted Answer

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

Question 19

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 20

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

Accepted Answer

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

Select the parametric equations matching with the following graph.

Using following result find a set of parametric equation of the line. Line: passes through (0,0) and

Find the standard form of the equation of the parabola with the given characteristics. Vertex: ; directrix:

Select the curve represented by the parametric equations. Cycloid:

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus:

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. A = (0,0), B = (3,4), C = (4,-3)

The -coordinate system has been rotated degrees from the -coordinate system.The coordinates of a point in the -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ,

Identify the conic by writing the equation in standard form.

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.

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

Select the graph of over the interval.Describe the part of the graph obtained in this case.

The -coordinate system has been rotated degrees from the -coordinate system.The coordinates of a point in the -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ,

Select the graph of the equation.

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. Earth miles

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. A = (-4,-5), B = (2,7), C = (5,7)

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 standard form of the equation of the ellipse with the following graph.

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

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

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Select the parametric equations matching with the following graph. ​ ​

Using following result find a set of parametric equation of the line. ​ ​ Line: passes through (0,0) and ​

Find the standard form of the equation of the parabola with the given characteristics. ​ Vertex: ; directrix: ​

Select the curve represented by the parametric equations. ​ Cycloid: ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus:

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​ A = (0,0), B = (3,4), C = (4,-3) ​

The -coordinate system has been rotated degrees from the -coordinate system.The coordinates of a point in the -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ​ , ​

Identify the conic by writing the equation in standard form. ​ ​

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. ​ ​

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

Select the graph of over the interval.Describe the part of the graph obtained in this case. ​ ​

The -coordinate system has been rotated degrees from the -coordinate system.The coordinates of a point in the -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ​ , ​

Select the graph of the equation. ​ ​

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. ​ Earth miles ​

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​ A = (-4,-5), B = (2,7), C = (5,7) ​

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 standard form of the equation of the ellipse with the following graph.

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

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

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Select the parametric equations matching with the following graph.

Using following result find a set of parametric equation of the line. Line: passes through (0,0) and

Find the standard form of the equation of the parabola with the given characteristics. Vertex: ; directrix:

Select the curve represented by the parametric equations. Cycloid:

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. A = (0,0), B = (3,4), C = (4,-3)

The -coordinate system has been rotated degrees from the -coordinate system.The coordinates of a point in the -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ,

Identify the conic by writing the equation in standard form.

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.

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

Select the graph of over the interval.Describe the part of the graph obtained in this case.

The -coordinate system has been rotated degrees from the -coordinate system.The coordinates of a point in the -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ,

Select the graph of the equation.

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. Earth miles

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. A = (-4,-5), B = (2,7), C = (5,7)

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.

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

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