Projecting the Tangent Point of an Ellipse
Let the tangent from a point on the axis to the ellipse with semimajor axis and semiminor axis touch at the point in the first quadrant. (The equation of the ellipse is .) Then the value of remains the same as changes.
 G. N. Berman, Problem Book in Mathematical Analysis, Moscow, Russia: Mir Publishers, 1957 p. 69.