# Thread: help with ellipse equation

1. ## 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

2. Originally Posted by doceye
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
$R_{flat} = \frac{(R_0 p)^2}{\sqrt{R_0^2 p}}$
if I have that right.

Then
$R_{flat} = \frac{R_0^2 p^2}{R_0 \sqrt{p}} = R_0 p^{3/2}$

$R_0 = \frac{R_{flat}}{p^{3/2}}$

But I'm having a hard time believing you can do the rest of what you did and not see how to do this. Is this what you wanted?

-Dan