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
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