So I have an ellipse where I know the two foci, the length and the width and all the relevant information. I then have a point somewhere in the ellipse. This point is known and an arbitrary angle ($\theta$) is known. I want to find the distance between the point in the ellipse and the side of the ellipse at the point along the angle. In the picture below is an example.
I want to find the distance between the $(1,-1)$ point and the $(x,y)$ point which is unknown. I'm not sure how to even begin this. Help is greatly appreciated.
The equation of your ellipse is: $\frac{x^2}{6^2}+\frac{y^2}{10^2}=1$.
Also from your picture, the pt at distance r away from (1,-1) is $(1+r\cos \theta, -1-r\sin \theta)$. Now you can solve $\frac{(1+r\cos \theta)^2}{6^2}+\frac{(-1-r\sin \theta)^2}{10^2}=1$ for r.
I get a quadratic equation in r: $ar^2+br+c=0$, where the coeff's a,b,c may depend on $\theta$.