# Exam: 250315RR - Conic Sections and Analytic Geometry

Exam: 250315RR - Conic Sections and Analytic Geometry

1. Convert the equation of the ellipse 5x

D. The equation isn't that of an ellipse.

2. What is the center of the hyperbola ?

A. (9,4)

B. (4,9)

C. (0,2)

D. (2,0)

3. Which of the following is the polar graph of ?

4. Express the parametric equations without the parameter.

5. A piece of string is hung from the points (-6,3) and (6,3) in the plane so that it hangs "down" (in the -y

direction) to just touch the origin at its vertex. How high above the x axis is the string over x = 2?

6. The eccentricity e tells you which of the following things about a conic section in polar coordinates?

A. Which type of conic section it is

B. Its orientation with respect to the pole

C. Whether it can be parameterized

D. How far its focus is from its directrix

7. A batter hits a baseball from 3 feet above home plate along the path x = 69t, y = 3 + 40t - 16t

How long is the ball in flight, and how far does it travel?

A.

B.

C.

D.

8. If the conic section Ax

A. A circle

B. A hyperbola

C. A parabola

D. An ellipse

9. What is the equation for the directrix of the parabola y

A. x = -5

B. x = 5

C. y = -5

D. y = 5x

10. Where are the foci for the ellipse ?

11. When is it possible to eliminate the parameter from a set of parametric equations?

A. Only when one equation is linear

B. Always

C. When you can isolate the parameter in one equation

D. When you have the original non-parametric form given

12. Translate the ellipse to be centered at (3, -1).

13. What kind of conic section is -6x

A. Circle

B. Parabola

C. Ellipse

D. Hyperbola

14. To determine which is the major axis of , which of these should you do?

A. Plug in 0 for x to find the y intercepts; these will be the vertices of the major axis.

B. Translate the ellipse to the origin using (-a,-b).

C. Find c using the relationship c

to determine the locations of the foci.

D. Compare a to b, and the larger goes with the major axis.

15. What are the substitution equations for rotating the axes back 30°?

16. What is the equation of the directrix for the conic section ?

A. x = –3

B. y = 6

C. x = 2

D. y = -6

17. Which of these is a valid geometric definition of a parabola?

A. The set of points equidistant from two foci

B. The set of points equidistant from two asymptotes that cross at the origin

C. The graph of y = x

End of exam

2

D. The set of points equidistant from a directrix and a focus not on the directrix

18. What is a parameterized version of the curve given by y - 3 = x + sin x?

A. t = x, sinx - y + 3

B. x = t, y = t + sint + 3

C. y = -3t, x = y + sint

D. t = - 3 = y, t + sint = x

19. What is the vertex of the parabola y

A. (0,0)

B. (-2,11)

C. (-11,2)

D. (2,11)

2

-4y -3x - 29 = 0?

20. If an ellipse has foci (±2,0) and vertices (±3,0), locate the vertices of its minor axis.

1. Convert the equation of the ellipse 5x

D. The equation isn't that of an ellipse.

2. What is the center of the hyperbola ?

A. (9,4)

B. (4,9)

C. (0,2)

D. (2,0)

3. Which of the following is the polar graph of ?

4. Express the parametric equations without the parameter.

5. A piece of string is hung from the points (-6,3) and (6,3) in the plane so that it hangs "down" (in the -y

direction) to just touch the origin at its vertex. How high above the x axis is the string over x = 2?

6. The eccentricity e tells you which of the following things about a conic section in polar coordinates?

A. Which type of conic section it is

B. Its orientation with respect to the pole

C. Whether it can be parameterized

D. How far its focus is from its directrix

7. A batter hits a baseball from 3 feet above home plate along the path x = 69t, y = 3 + 40t - 16t

How long is the ball in flight, and how far does it travel?

A.

B.

C.

D.

8. If the conic section Ax

A. A circle

B. A hyperbola

C. A parabola

D. An ellipse

9. What is the equation for the directrix of the parabola y

A. x = -5

B. x = 5

C. y = -5

D. y = 5x

10. Where are the foci for the ellipse ?

11. When is it possible to eliminate the parameter from a set of parametric equations?

A. Only when one equation is linear

B. Always

C. When you can isolate the parameter in one equation

D. When you have the original non-parametric form given

12. Translate the ellipse to be centered at (3, -1).

13. What kind of conic section is -6x

A. Circle

B. Parabola

C. Ellipse

D. Hyperbola

14. To determine which is the major axis of , which of these should you do?

A. Plug in 0 for x to find the y intercepts; these will be the vertices of the major axis.

B. Translate the ellipse to the origin using (-a,-b).

C. Find c using the relationship c

to determine the locations of the foci.

D. Compare a to b, and the larger goes with the major axis.

15. What are the substitution equations for rotating the axes back 30°?

16. What is the equation of the directrix for the conic section ?

A. x = –3

B. y = 6

C. x = 2

D. y = -6

17. Which of these is a valid geometric definition of a parabola?

A. The set of points equidistant from two foci

B. The set of points equidistant from two asymptotes that cross at the origin

C. The graph of y = x

End of exam

2

D. The set of points equidistant from a directrix and a focus not on the directrix

18. What is a parameterized version of the curve given by y - 3 = x + sin x?

A. t = x, sinx - y + 3

B. x = t, y = t + sint + 3

C. y = -3t, x = y + sint

D. t = - 3 = y, t + sint = x

19. What is the vertex of the parabola y

A. (0,0)

B. (-2,11)

C. (-11,2)

D. (2,11)

2

-4y -3x - 29 = 0?

20. If an ellipse has foci (±2,0) and vertices (±3,0), locate the vertices of its minor axis.

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