# Geo5.2.43

From Example Problems

P is a point on the ellipse and Q is its corresponding point on the auxiliary circle. Prove that the locus of the point of intersection of the normals at P and Q is the circle given by

Equation to the normal at on the ellipse is

P1 is the corresponding point on

Therefore,equation to the normal to auxiliary circle is

From the above,

Eliminating theta from the equation of normal,we get

Therefore,the locus of the first two equations is