What is the directrix for a polar conic with the given equation?

[Jbreezy]

Homework Statement

Hi wondering what the directrix is for this

Homework Equations

r = (20)/ (2+sin(theta))

The Attempt at a Solution

I factored denominator so it read 2(1+ (1/2)sin(theta)) ...So I said e times d = (2/20) and I got d = (1/5) because e is (1/2). Doesn't make sense though seems to small because that lies inside of the thing when I graph it.

 

[Simon Bridge]

I factored denominator so it read 2(1+ (1/2)sin(theta)) ...So I said e times d = (2/20) and I got d = (1/5) because e is (1/2). Doesn't make sense though seems to small because that lies inside of the thing when I graph it.

This bit you did OK - try working on the whole fraction though.
$$r=\frac{20}{2+\sin\theta} = \frac{10}{1+\frac{1}{2}\sin\theta}=\frac{ed}{1+e\sin\theta}$$

So $e=\frac{1}{2}$ right? And $ed=\cdots$?

 

[Jbreezy]

d = 20? ed = 10 = (1/2) = 10

 

[Simon Bridge]

d = 20? ed = 10 = (1/2) = 10

Um... that is just nonsense. eg. 10 ≠ (1/2)

You have to use reasonable grammar when you write sentences in any language.
Math is also a language - therefore you should take some trouble to make sure the math/number sentences you write down actually mean something.

Want to try again?