Question

A Variable Tangent To The Ellipse (x/a)^2 + (y/b)^2 =1 meets the parabola y^2=4ax at L and M. Find the locus of the midpoint of L M

Answer 1

Man. some messy algebra! Clearly there are horizontal asymptotes at y = ±b and curve passes through (a,0).

The shape seems to preclude any simple equation or parametric equations. Maybe more later.