Question 1

Find the inclination Θ (in degrees) of the line with a slope of m.Round your answer to one decimal places. ​   ​

Accepted Answer

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

Question 2

A straight road rises with an inclination of 0.21 radian from the horizontal (see figure).Find the slope of the road and the change in elevation (x) over a two-mile stretch of the road.Round your answer to four decimal places for the m round your answers to nearest whole number for change in elevation. ​   ​   ​

Accepted Answer

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

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 curve represented by the parametric equations. ​
Cycloid:   ​

Accepted Answer

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

Question 5

Select the curve represented by the parametric equations. ​     ​

Accepted Answer

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

Question 6

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:

Question 7

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

Accepted Answer

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

Question 8

Find the center and the vertices of the ellipse. ​   ​

Accepted Answer

A) center: (-9, 9); vertices: (-1, -9), (1, 9) 
B) center: (0, 0); vertices: (0, -9), (0, 9) 
C) center: (0, 0); vertices: (-9, -1), (9, 1) 
D) center: (0, 0); vertices: (-9, 0), (9, 0) 
E) center: (-9, 9); vertices: (-1, 0), (1, 0) 
A) center: (-9, 9); vertices: (-1, -9), (1, 9) 
B) center: (0, 0); vertices: (0, -9), (0, 9) 
C) center: (0, 0); vertices: (-9, -1), (9, 1) 
D) center: (0, 0); vertices: (-9, 0), (9, 0) 
E) center: (-9, 9); vertices: (-1, 0), (1, 0)

Question 9

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

Accepted Answer

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

Question 10

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

Question 11

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

Accepted Answer

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

Question 12

Use a graphing utility to graph the parabola.   ​

Accepted Answer

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

Question 13

Select the graph for following equation. ​   ​

Accepted Answer

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

Question 14

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 15

A simply supported beam is 12 meters long and has a load at the center (see figure). ​   ​
Where,   The deflection of the beam at its center is 2 centimeters.Assume that the shape of the deflected beam is parabolic.Write an equation of the parabola.(Assume that the origin is at the center of the deflected beam.)
​

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​
Focus: (0,-2)
​

Accepted Answer

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

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 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 20

Select the graph of degenerate conic. ​   ​

Accepted Answer

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

Find the inclination Θ (in degrees) of the line with a slope of m.Round your answer to one decimal places.

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 curve represented by the parametric equations. Cycloid:

Select the curve represented by the parametric equations.

Find the center and vertices of the ellipse.

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

Find the center and the vertices of the ellipse.

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

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

Identify the conic by writing the equation in standard form.

Use a graphing utility to graph the parabola.

Select the graph for following equation.

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

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

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: (0,-2)

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

Select the graph of degenerate conic.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Find the inclination Θ (in degrees) of the line with a slope of m.Round your answer to one decimal places. ​ ​

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 curve represented by the parametric equations. ​ Cycloid: ​

Select the curve represented by the parametric equations. ​ ​

Find the center and vertices of the ellipse. ​ ​

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

Find the center and the vertices of the ellipse. ​ ​

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

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

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

Use a graphing utility to graph the parabola. ​

Select the graph for following equation. ​ ​

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

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

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​ Focus: (0,-2) ​

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

Select the graph of degenerate conic. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Find the inclination Θ (in degrees) of the line with a slope of m.Round your answer to one decimal places.

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 curve represented by the parametric equations. Cycloid:

Select the curve represented by the parametric equations.

Find the center and vertices of the ellipse.

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

Find the center and the vertices of the ellipse.

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

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

Identify the conic by writing the equation in standard form.

Use a graphing utility to graph the parabola.

Select the graph for following equation.

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

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

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: (0,-2)

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

Select the graph of degenerate conic.