Chords at right angles are drawn through any point p(m) of the ellipse and the line joining their extremitiesmeets the normal in the point Q. Prove thatQ is same for all such chords its coordinates being a3e2cosm/(a2+b2) , -a2be2sinm/((a2+b2) .Also prove that the major axis is the bisector of the angle PCQ and locus of Q for different positions of P is the ellipse x2/a2 +y2/b2 = (a2-b2)2/(a2+b2)2

Avinash , 6 Years ago

Grade 12