Maximum value of the square of length of chord of the ellipse x28+y24=1, such that eccentric angles of its
extremities differ by π2 is
Let P≡(22cosθ,2sinθ)Q≡(−22sinθ,2cosθ)(PQ)2=8(cosθ+sinθ)2+4(sinθ−cosθ)2
=12+4sin2θ≤16∴(PQ)2max=16