CLICK HERE TO DOWNLOAD THIS ANSWER INSTANTLY $9.50 Only
1. Express the parametric equations without the parameter.
2. Eliminate the parameter from the parametric form of the following equation.
3. To determine which is the major axis of , which of these should you do?
A. Translate the ellipse to the origin using (−a,−b).
B. Plug in 0 for x to find the y intercepts; these will be the vertices of the major axis.
C. Compare a to b, and the larger goes with the major axis.
D. Find c using the relationship c 2 = a 2 + b 2 to determine the locations of the foci.
4. What is the focus of the parabola x2 = −4y?
A. (0,−1)
B. (−1,0)
C. (1,0)
D. (0,1)
5. The eccentricity e tells you which of the following things about a conic section in polar coordinates?
A. How far its focus is from its directrix
B. Whether it can be parameterized
C. Its orientation with respect to the pole
D. Which type of conic section it is
6. What is a parameterized version of the curve given by y − 3 = x + sin x?
A. y = −3t, x = y + sint
B. t = x, sinx − y + 3
C. t = − 3 = y, t + sint = x
D. x = t, y = t + sint + 3
7. What is the equation of the directrix for the conic section ?
A. x = 2
B. y = −6
C. y = 6
D. x = –3
8. Translate the ellipse to be centered at (3, −1).
A.
B.
C.
D.
9. How many asymptotes does a hyperbola have?
A. 0
B. 1
C. 2
D. 3
10. What is the vertex of the parabola y2 −4y −3x − 29 = 0?
A. (0,0)
B. (−2,11)
C. (−11,2)
D. (2,11)
11. Which of the following is the polar graph of ?
12. What kind of conic section is −6x2 + 9xy − 3y2 + 11x − 6y + 1 = 0?
A. Circle
B. Parabola
C. Ellipse
D. Hyperbola
13. When is it possible to eliminate the parameter from a set of parametric equations?
A. Always
B. Only when one equation is linear
C. When you have the original non-parametric form given
D. When you can isolate the parameter in one equation
14. What are the substitution equations for rotating the axes back 30°?
15. Which conic section is comprised of two branches?
A. Hyperbola
B. Parabola
C. Ellipse
D. Circle
16. 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?
A. 1/4
B. 1/3
C. 1/6
D. 1/5
17. Where are the foci for the ellipse ?
18. What is the equation for the directrix of the parabola y2 = 20x?
A. x = 5
B. y = 5x
C. y = −5
D. x = −5
19. Which of these is a valid geometric definition of a parabola?
A. The graph of y = x2
B. The set of points equidistant from two foci
C. The set of points equidistant from a directrix and a focus not on the directrix
D. The set of points equidistant from two asymptotes that cross at the origin
20. What is the center of the hyperbola ?
A. (0,2)
B. (9,4)
C. (2,0)
D. (4,9)
