A neat little demo of an algorithm that finds the intersection of a line and an ellipse. Click and drag to move the line.
http://quickcalcbasic.com/ellipse%20line%20intersection.pdf https://math.stackexchange.com/questions/2645689/what-is-the-parametric-equation-of-a-rotated-ellipse-given-the-angle-of-rotatio#2647450