If tan θ 1 × tan θ 2 = - a 2 b 2 , then the chord joining 2 points θ 1 and θ 2 on the ellipse x 2 a 2 + y 2 b 2 = 1 will subtend a right angle at

Step-by-step solution

Let the two points be A a cos θ 1 , b sin θ 1   &   B a cos θ 2 , b sin θ 2 O 0 , 0 is origin Slope of O A = b sin θ 1 a cos θ 1 = b tan θ 1 a Slope of O B = b sin θ 2 a cos θ 2 = b tan θ 2 a Slope of O A × Slope of O B = b 2 a 2 tan θ 1 tan θ 2 = - 1 Therefore, chord subtends the right angle at center.