Parametrisation of an ellipse in polar coordinates If we have an ellipse with equation $x^2/a^2+y^2/b^2=1$ then if we were to change this into polar coordinates then  would the parametrisation be $x=ar\cos(\theta)$ and $y=br\sin(\theta)$?
Also what would the parametrisation of a hyperbola be?

Parameterization and Conversion to Polar coordinate are not linked
To parameterize hyperbola $$\frac{(x-\alpha)^2}{a^2}-\frac{(y-\beta)^2}{b^2}=1\text{ and }\sec^2\phi-\tan^2\phi=1$$
$$\frac{x-\alpha}a=\sec\phi, \frac{y-\beta}b=\tan\phi$$
For  Conversion to Polar coordinate always $$x=r\cos\theta,y=r\sin\theta$$
