Geometric Constructions

E-mail: jay(at)salsburg(dot)com

CAD Challange - In the image below, 2 ellipses are arbitrarily oriented close to a straight line. If the 2 ellipses' foci coordinates and min/max dimensions are known, show the method used to compute the 2 end coordinates of the straight line's best tangent to the 2 ellipses. Also show the method of computing the 2 coordinates of the points where the line crosses the envelope of the 2 ellipses. A parametric solution is preferred but not necessary.

Givens:

Ellipse #1 - Foci 1 & 2 coordinates, length of Maximum Axis, length of Minimum Axis

Ellipse #2 - Foci 1 & 2 coordinates, length of Maximum Axis, length of Minimum Axis

Length of line