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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 a 3 e 2 cosm/(a 2 +b 2 ) , -a 2 be 2 sinm/((a 2 +b 2 ) . 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 x 2 /a 2 +y 2 /b 2 = (a 2 -b 2 ) 2 /(a 2 +b 2 ) 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

Grade:12

1 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

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