8.08, part 2

11. find an equation in standard form for the hyperbola with vertices at (0, ±6) and foci at (0, ±9).

a) y squared over 45 minus x squared over 36 = 1
b) y squared over 81 minus x squared over 36 = 1
c) y squared over 36 minus x squared over 81 = 1
d) y squared over 36 minus x squared over 45 = 1

12. find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ± 1 divided by 4. x.

a) y squared over 16 minus x squared over 64 = 1
b) y squared over 16 minus x squared over 256 = 1
c) y squared over 256 minus x squared over 16 = 1
d) y squared over 64 minus x squared over 4 = 1

13. eliminate the parameter.
x = t - 3, y = t2 + 5

a) y = x2 + 6x + 14
b) y = x2 - 14
c) y = x2 - 6x - 14
d) y = x2 + 14

14. find the rectangular coordinates of the point with the polar coordinates.
ordered pair 3 comma 2 pi divided by 3

a) ordered pair negative 3 divided by 2 comma 3 square root 3 divided by 2
b) ordered pair 3 square root 3 divided by 2 comma negative 3 divided by 2
c) ordered pair negative 3 divided by 2 comma 3 divided by 2
d) ordered pair 3 divided by 2 comma negative 3 divided by 2

15. find all polar coordinates of point p where p = negative pi divided by 6 .

a) (1, negative pi divided by 6 + (2n + 1)π) or (-1, negative pi divided by 6 + 2nπ)
b) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ)
c) (1, negative pi divided by 6 + 2nπ) or (1, pi divided by 6 + (2n + 1)π)
d) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + (2n + 1)π)

16. determine two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°.

a) (4 square root 2 , 135°), (-4 square root 2 , 315°)
b) (4 square root 2 , 45°), (-4 square root 2 , 225°)
c) (4 square root 2 , 315°), (-4 square root 2 , 135°)
d) (4 square root 2 , 225°), (-4 square root 2 , 45°)

17. the graph of a limacon curve is given. without using your graphing calculator, determine which equation is correct for the graph.
a circular graph with an inner loop on the left

[-5, 5] by [-5, 5] (5 points)

a) r = 3 + 2 cos θ
b) r = 2 + 3 cos θ
c) r = 2 + 2 cos θ
d) r = 4 + cos θ

18. determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = -2 + 3 cos θ

a) no symmetry
b) y-axis only
c) x-axis only
d) origin only

19. a railroad tunnel is shaped like a semiellipse, as shown below.
a semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis.

the height of the tunnel at the center is 54 ft, and the vertical clearance must be 18 ft at a point 8 ft from the center. find an equation for the ellipse.

20. determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 2 cos 3θ