Question

How do we derive the general polar form of an ellipse, given that a,b are the semi-diameters, and φ is the angle between a and the polar axis.

Answer 1

According to wiki, the equation should be:
\[r(\theta) = \frac{P(\theta)+Q(\theta)}{R(\theta)}\]where:\[P( \theta) = r_{0}[(b^{2}-a^{2})cos( \theta + \theta_{0} - 2 \phi)+(a^{2}+b^{2})cos( \theta - \theta_{0})]\]\[Q( \theta) = \sqrt{2}ab \sqrt{R( \theta) - 2r_{0}^{2}sin^{2}( \theta - \theta_0)}\]\[R( \theta) = (b^{2}-a^{2}cos(2 \theta - 2 \phi) + a^{2} + b^{2}\]But I would like to see how this is derived.

Answer 2

or even a confirmation that that's the right equation.