Show that the equation of the auxiliary circle of the ellipse is .
The equation to the ellipse is
The equation to the tangent of the ellipse is
The equation to the perpendicular from either focus on this tangent is given by
To find the locus of point of intersection of the above two equations,eliminate m from them.
Squaring and adding the two equations,we get
Therefore the locus is the auxiliary circle concentric with the ellipse.