I need to derive the ellipses polar equation relative to one of it's foci.
My starting point is the ellipses polar equation relative to the ellipses center:
$$r(\theta) = \frac{a·b}{\sqrt({(b·cos( \theta ) + (a·cos( \theta))}}\tag 1$$
From equation $(1)$, I want to derive the ellipses polar equation relative to one of it's foci, which is given by: $$r(\theta) = \frac{a·(1-e^2)}{1+- e·cos(\theta)} \tag 2$$
I want to know how to derive equation $(2)$ from equation $(1)$.