Calculating X & Y coordinates of a point offset from an ellipse at a given polar angle and intersecting point

Question

I am using the following equations to identify the x and y coordinates of a point on an ellipse at polar angle θ.

$x=\pm\cfrac{ab}{\sqrt{b^2+a^2 (\tan^2\theta)}}$

$y=\pm\cfrac{ab}{\sqrt{a^2+b^2 (\tan^2\theta)}}$

Perpendicular to this point on the ellipse I would like to calculate the X and Y coordinates at an outside offset distance of d.

Effectively, I am trying to identify points on a parallel curve to the ellipse.

Any and all assistance is much appreciated!