Question

r=4/(-2-6sinϴ)

1. What is the eccentricity of the function?
2. What is the distance between the pole and the directrix?

1. A. 2
B. -2
C. 3
D. -3

2. A. 2
B. 2/3
C. 3
D. 6

Answer 1

So, I guess you did not read the web page I suggested ...

r = ed/(1+e sin?)

r=4/(-2-6sin?)
r = -2/(1+3sin?)
so, e=3 and d=2/3

in x-y coordinates, that is

(y-3/4)^2 - x^2/8 = 1/16

http://www.wolframalpha.com/input/?i=hyperbola+(y-3%2F4)%5E2+-+x%5E2%2F8+%3D+1%2F16

You can see that with a focus at (0,0), vertex at (0,1/2) and eccentricity of 3 it agrees with the information from the polar form.