The tangent at any point P on the ellipse x2-a2-y2-b2-1 meets the auxiliary circle in two points which subtend right angle at the centre of the ellipse- If - be the eccentric angle of P and e be the eccentricity of the ellipse- then sin-A- -1- e 2 - eB- e - -1- e 2C- -1-e2D- None of these

The correct option is A √(1 e^2)/e nbsp; ...

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Standard XII

Mathematics

Circular Measurement of Angle

The tangent a...

Question

The tangent at any point P on the ellipse meets the auxiliary

circle in two points which subtend right angle at the centre of the ellipse. If θ be the eccentric angle of P and e be the eccentricity of the ellipse, then sinθ =

\sqrt{1 - e^{2}}

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e / \sqrt{1 - e^{2}}

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\sqrt{1 - e^{2}} / e

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None of these

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Solution

The correct option is C $\sqrt{1 - e^{2}} / e$

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Similar questions

Q. The tangent at any point P on the ellipse

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e

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If the tangent at $θ$ on the ellipse $x^{2} / a^{2} + y^{2} / b^{2} = 1$ meets the auxiliary circle at two point which subtended a right angle at
the centre, then $e^{2} (2 - c o s^{2} θ) =$

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The tangent at any point P on the ellipse meets the auxiliary circle in two points which subtend right angle at the centre of the ellipse. If θ be the eccentric angle of P and e be the eccentricity of the ellipse, then sinθ =

The correct option is C √1−e2/e

The tangent at any point P on the ellipse meets the auxiliary

circle in two points which subtend right angle at the centre of the ellipse. If θ be the eccentric angle of P and e be the eccentricity of the ellipse, then sinθ =

The correct option is C $\sqrt{1 - e^{2}} / e$