8.07a, part 2

10. graph the hyperbola with equation quantity x minus 1 squared divided by 49 minus the quantity of y plus 3 squared divided by 9 equals 1 .

a) a horizontal hyperbola is shown on the coordinate plane centered at the origin with vertices at the point negative seven comma zero and seven comma zero.
b) a vertical hyperbola is shown on the coordinate plane centered at the origin with vertices at the point zero comma seven and zero comma negative seven.
c) a horizontal hyperbola is shown on the coordinate plane centered at the point one comma negative three with vertices at the point negative six comma negative three and eight comma negative three.
d) a vertical hyperbola is shown on the coordinate plane centered at the point negative one comma three with vertices at the point negative one comma ten and negative one comma four.

11. find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11).

a) y squared over 4 minus x squared over 117 equals 1
b) y squared over 4 minus x squared over 121 equals 1
c) y squared over 121 minus x squared over 4 equals 1
d) y squared over 117 minus x squared over 4 equals 1

12. find an equation in standard form for the hyperbola with vertices at (0, ±8) and asymptotes at y equals plus or minus 1 half x . (1 point)

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

13. eliminate the parameter.
x = t - 3, y equals two divided by quantity t plus five

a) y equals two divided by quantity negative x plus eight
b) y equals two divided by quantity x plus two
c) y equals two divided by quantity x plus five
d) y equals two divided by quantity x plus eight

14. find the rectangular coordinates of the point with the polar coordinates ordered pair 7 comma 2 pi divided by 3 .

a) ordered pair negative 7 divided by 2 comma 7 square root 3 divided by 2
b) ordered pair negative 7 divided by 2 comma 7 divided by 2
c) ordered pair 7 divided by 2 comma negative 7 divided by 2
d) ordered pair 7 square root 3 divided by 2 comma negative 7 divided by 2

15. find all polar coordinates of point p where p = ordered pair 1 comma pi divided by 3 .

a) (1, pi divided by 3 + 2nπ) or (-1, pi divided by 3 + (2n + 1)π)
b) (1, pi divided by 3 + (2n + 1)π) or (-1, pi divided by 3 + 2nπ)
c) (1, pi divided by 3 + nπ) or (-1, pi divided by 3 + nπ)
d) (1, pi divided by 3 + 2nπ) or (-1, pi divided by 3 + 2nπ)

16. determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°.

a) (3 square root of 2 , 315°), (-3 square root of 2 , 135°)
b) (3 square root of 2 , 225°), (-3 square root of 2 , 45°)
c) (3 square root of 2 , 45°), (-3 square root of 2 , 225°)
d) (3 square root of 2 , 135°), (-3 square root of 2 , 315°)

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 indentation on the left toward the origin, but not touching the origin

[-5, 5] by [-5, 5]

a) r = 2 + 3 cos θ
b) r = 3 + 2 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 = 4 - 4 cos θ

a) no symmetry
b) x-axis only
c) y-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 58 ft, and the vertical clearance must be 29 ft at a point 21 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 = 4 cos 5θ