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 that Q 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
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 that Q 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 , 7 Years ago
Grade 12
