Three points A, B, C are taken, on an ellipse, with eccentr…

Maths Conic Sections Ellipse Numeric Response

Published on: August 13, 2026

Three points A, B, C are taken, on an ellipse, with eccentric angles θ, θ + α and θ + 2 α . Find α (in degrees) for which area of Δ ABC is max.

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The correct answer is:

Ans. 0120

Sol. Area of Δ ABC with vertices

(a cos θ , b sin θ ) (a cos ( θ + α ), b sin ( θ + α ))

and (a cos ( θ + 2 α ), b sin ( θ + 2 α ))

= ab

= ab sin

= 2ab sin 2

= 2ab sin 2 sin α

Δ = ab sin α (1 – cos α ) = [2 sin α – sin 2 α ]

for maximum sin 2 α must be negative and sin α is positive on solving if we get α = 120°

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