# Geo5.2.41

From Example Problems

Tangents at right angles are drawn to the ellipse.Show that the locus of the midpoints of chords of contact is the curve

Let be the mid point of a chord QR of the given ellipse.

Equation to chord QR is

(say)

Let the tangents at Q and R to the ellipse meet at M.

Therefore coordinates of M are

Given that the tangents MQ and MR are perpendiculars.

Mlies on director circle

Therefore the locus of P is