How do I find the pole and directrix? And then what do I do to find the distance between them? - Thanks.

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Expert Answers
gsenviro eNotes educator| Certified Educator

To determine the distance between the pole and the directrix, you do not need to find the pole and directrix. 

The polar form of equation of a conic (for horizontal directrix) can be written as:

r = ` ke/(1+-e sintheta)`

where, k is the distance between the pole and the directrix

We can rewrite the given equation of r to this format.

r = `4/(-2-6 sintheta)`

Dividing the numerator and denominator by -2, we get

r = `-2/(1+3 sintheta)`

Comparing with the standard equation, e = 3 and k = 2/3 .

Thus, the distance between the pole and the directrix for the given case is 2/3.