help with ellipse equation

Hi,

I've got an ellipse defined by a central (steep) radius of curvature (R0) and a p-value (shape factor) that is p=1-e^2

I've derived most of the formulas I need for calculating the local radius of curvature at given points. One problem I don't seem to be able to solve is the definition of the ellipse via the flat radius of curvature.

The p-values I've got define the radius of the ellipse at its steep apex and from there it becomes flatter.

I would want to define the ellipse via its flat radius and become steeper from there.

I know that

a = R0 * p

b = SQRT(R0^2*p)

Rflat = a^2/b

so Rflat = (R0 * p)^2 / SQRT R0*p)

can someone derive the expression for Rsteep as a function of Rflat and p?

thanks heaps