Given 4 / (-2 - 6sin (theta)) What is the distance between the pole and the directrix?

2/3

Step-by-step explanation:

For a conic equation of the form ...

r = ed / (1+e·sin (θ))

the eccentricity is represented by e and the distance from the pole to the directrix is represented by d.

Your equation can be rewritten in this form as ...

r = 3· (-2/3) / (1 + 3·sin (θ))

This means the directrix is 2/3 units below the pole.