Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

A straight road rises with an inclination of 0.22 radian from the horizontal.Find the slope of the road and the change in elevation over a one-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 4

Select correct graph to graph rotated conic. ​   ​

Accepted Answer

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

Question 5

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

Accepted Answer

A) ​   Entire circle 
B) ​   Entire circle 
C) ​   Entire circle 
D) ​   Entire circle 
E) ​   Entire circle 
A) ​   Entire circle 
B) ​   Entire circle 
C) ​   Entire circle 
D) ​   Entire circle 
E) ​   Entire circle

Question 6

Find the standard form of the equation of the ellipse with the given characteristics. ​
Foci:   , endpoints of the major axis:   ​

Accepted Answer

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

Question 7

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 8

Select the polar equation of graph. ​   ​

Accepted Answer

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

Question 9

The Roman Coliseum is an elliptical amphitheater measuring approximately 188 meters long and 156 meters wide.Find an equation to model the coliseum that is of the form ​   .
​

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

A projectile is launched at a height of h feet above the ground at an angle of   with the horizontal.The initial velocity is   feet per second, and the path of the projectile is modeled by the parametric equations   . Select the correct graph of the path of a projectile launched from ground level at the value of   and   .
​   feet per second
​

Accepted Answer

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

Question 12

Use the discriminant to classify the graph. ​   ​

Accepted Answer

A) The graph is a parabola. 
B) The graph is a hyperbola. 
C) The graph is a line. 
D) The graph is a circle. 
E) The graph is a ellipse. 
A) The graph is a parabola. 
B) The graph is a hyperbola. 
C) The graph is a line. 
D) The graph is a circle. 
E) The graph is a ellipse.

Question 13

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

Accepted Answer

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

Question 14

Find the center and vertices of the hyperbola.

Accepted Answer

A) center: (3, -2), vertices: (3, -4), (3, 0) 
B) center: (-3, 2), vertices: (-3, 0), (-3, 4) 
C) center: (3, -2), vertices: (1, -2), (5,-2) 
D) center: (2, -3), vertices: (0, -3), (4, -3) 
E) center: (-3,2), vertices: (-5, 2), (-1, 2) 
A) center: (3, -2), vertices: (3, -4), (3, 0) 
B) center: (-3, 2), vertices: (-3, 0), (-3, 4) 
C) center: (3, -2), vertices: (1, -2), (5,-2) 
D) center: (2, -3), vertices: (0, -3), (4, -3) 
E) center: (-3,2), vertices: (-5, 2), (-1, 2)

Question 15

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Vertices: (0,±7); focies: (0,±4)
​

Accepted Answer

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

Question 16

Select correct graph to graph rotated conic. ​   ​

Accepted Answer

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

Question 17

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 18

Find the standard form of the equation of the ellipse with vertices   and eccentricity   .

Accepted Answer

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

Question 19

A point in rectangular coordinates is given.Convert the point to polar coordinates.Round your answers to two decimal places, 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 20

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

Accepted Answer

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

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.

A straight road rises with an inclination of 0.22 radian from the horizontal.Find the slope of the road and the change in elevation over a one-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.

Select correct graph to graph rotated conic.

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

Find the standard form of the equation of the ellipse with the given characteristics. Foci: , endpoints of the major axis:

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

Select the polar equation of graph.

The Roman Coliseum is an elliptical amphitheater measuring approximately 188 meters long and 156 meters wide.Find an equation to model the coliseum that is of the form .

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

Use the discriminant to classify the graph.

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

Find the center and vertices of the hyperbola.

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: (0,±7); focies: (0,±4)

Select correct graph to graph rotated conic.

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. ,

Find the standard form of the equation of the ellipse with vertices and eccentricity .

A point in rectangular coordinates is given.Convert the point to polar coordinates.Round your answers to two decimal places, r > 0.

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

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

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. ​ ​

A straight road rises with an inclination of 0.22 radian from the horizontal.Find the slope of the road and the change in elevation over a one-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. ​

Select correct graph to graph rotated conic. ​ ​

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

Find the standard form of the equation of the ellipse with the given characteristics. ​ Foci: , endpoints of the major axis: ​

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

Select the polar equation of graph. ​ ​

The Roman Coliseum is an elliptical amphitheater measuring approximately 188 meters long and 156 meters wide.Find an equation to model the coliseum that is of the form ​ . ​

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

Use the discriminant to classify the graph. ​ ​

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

Find the center and vertices of the hyperbola.

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Vertices: (0,±7); focies: (0,±4) ​

Select correct graph to graph rotated conic. ​ ​

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. ​ , ​

Find the standard form of the equation of the ellipse with vertices and eccentricity .

A point in rectangular coordinates is given.Convert the point to polar coordinates.Round your answers to two decimal places, r > 0. ​ ​

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

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

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.

A straight road rises with an inclination of 0.22 radian from the horizontal.Find the slope of the road and the change in elevation over a one-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.

Select correct graph to graph rotated conic.

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

Find the standard form of the equation of the ellipse with the given characteristics. Foci: , endpoints of the major axis:

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

Select the polar equation of graph.

The Roman Coliseum is an elliptical amphitheater measuring approximately 188 meters long and 156 meters wide.Find an equation to model the coliseum that is of the form .

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

Use the discriminant to classify the graph.

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

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: (0,±7); focies: (0,±4)

Select correct graph to graph rotated conic.

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. ,

A point in rectangular coordinates is given.Convert the point to polar coordinates.Round your answers to two decimal places, r > 0.

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