If the tangent at a point $(a\cos heta,\ b\sin{ heta)}$ on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ meets the auxiliary circle in two points, the chord joining them subtends a right angle at the centre, then the eccentricity of the ellipse is given by

Question

If the tangent at a point $(a\cos	heta,\ b\sin{	heta)}$ on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ meets the auxiliary circle in two points, the chord joining them subtends a right angle at the centre, then the eccentricity of the ellipse is given by

Dr. Abubacker · Accepted Answer

The correct answer is Option B: $(1 + \sin^{2}	heta)$.

Q. If the tangent at a point $(a\cos\theta,\ b\sin{\theta)}$ on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ meets the auxiliary circle in two points, the chord joining them subtends a right angle at the centre, then the eccentricity of the ellipse is given by

Explanation

Reviewed by Dr. Abubacker

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