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If P(alpha,beta) is a point on the ell...

If `P(alpha,beta)` is a point on the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` with foci `S a n d S '` and eccentricity `e ,` then prove that the area of Δ` S P S '` is `be sqrt(a^2-alpha^2)`

A

`ae sqrt(a^(2) - alpha^(2))`

B

`be sqrt(b^(2) - alpha^(2))`

C

`ae sqrt(b^(2) - alpha^(2))`

D

`be sqrt(a^(2) - alpha^(2))`

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-ELLIPSE-Chapter Test
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  2. If (-4, 3) and (8, 3) are the vertices of an ellipse whose eccentricit...

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  3. If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^...

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  4. If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1...

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  5. The tangent at any point P on the ellipse meets the tangents at the ve...

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  6. P is a point on the circle x^(2) + y^(2) = c^(2). The locus of the mid...

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  7. The equation of the locus of the poles of normal chords of the ellipse...

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  8. The locus of mid-points of focal chords of the ellipse (x^2)/(a^2)+(y^...

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  9. The locus of a point whose polar with respect to the ellipse (x^2)/(a^...

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  10. if the chord of contact of tangents from a point P to the hyperbola x...

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  11. The locus of the poles of tangents to the auxiliary circle with respec...

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  12. The locus of the poles of tangents to the director circle of the ellip...

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  13. P is a point on the circle x^(2) + y^(2) = c^(2). The locus of the mid...

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  14. If the tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 makes inte...

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  15. If the tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 make angles a...

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  16. If C is centre of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and the no...

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  17. If the normals at P(theta) and Q(pi/2+theta) to the ellipse (x^2)/(a^2...

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  18. about to only mathematics

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  19. The tangent at point P on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 cu...

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  20. If the lengths of major and semi-minor axes of an ellipse are 4 and sq...

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