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CGP EDU Academic Team
Published on: August 13, 2026
The tangent at a point P (acos θ θ , bsin θ θ ) on the ellipse 
meets the auxiliary circle in two points. The chord joining them subtends a right angle at the center. Then the eccentricity of the ellipse is given by
Text Solution
Verified by ExpertsThe correct answer is:
A
The lines given by this equation are at right angles.
∴ ∴ coefficient of x 2 + coefficient of y 2 = 0
⇒ ⇒ 
⇒ ⇒ sin 2 θ θ + 1-
⇒ ⇒ sin 2 θ θ + 
⇒ ⇒ = sin 2 θ θ (a 2 -b 2 )+b 2 = 0
⇒ ⇒ 
⇒ ⇒ 1 = e 2 (1+sin 2 θ θ )
⇒ ⇒ e = (1+sin 2 θ θ ) -1/2 .
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