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Let Sa n dS ' be two foci of the ellipse...

Let `Sa n dS '` be two foci of the ellipse `(x^2)/(a^3)+(y^2)/(b^2)=1` . If a circle described on `S S^(prime)` as diameter intersects the ellipse at real and distinct points, then the eccentricity`e` of the ellipse satisfies `c=1/(sqrt(2))` (b) `e in (1/(sqrt(2)),1)` `e in (0,1/(sqrt(2)))` (d) none of these

A

`2 // sqrt3`

B

`sqrt3//2`

C

`1// sqrt2`

D

`1//sqrt3`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA-ELLIPSE-Chapter Test
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  2. If the minor axis of an ellipse subtends an angle of 60^(@) at each fo...

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  3. Let Sa n dS ' be two foci of the ellipse (x^2)/(a^3)+(y^2)/(b^2)=1 . I...

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  4. The equation of the normal at the point P (2, 3) on the ellipse 9x^(2)...

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  5. For the ellipse 3x^(2) + 4y^(2) + 6x - 8y - 5 = 0 the eccentrically, i...

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  6. Let S, S' be the focil and BB' be the minor axis of the ellipse (x^(2)...

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  7. If the length of the latusrectum of the ellipse x^(2) tan^(2) theta + ...

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  8. if vertices of an ellipse are (-4,1),(6,1) and x-2y=2 is focal chord t...

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  9. If (-4, 3) and (8, 3) are the vertices of an ellipse whose eccentricit...

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  10. The area of the triangle formed by three points on the ellipse x^2/a^2...

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  11. If the chord joining points P(alpha)a n dQ(beta) on the ellipse ((x...

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

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

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

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  15. The locus of the poles of normal chords of the ellipse x^(2)/a^(2) + y...

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  16. The locus of mid-points of a focal chord of the ellipse x^2/a^2+y^2/b^...

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  17. The locus of points whose polars with respect to the ellipse x^(2)/a^(...

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

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

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

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