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If e(1) is the eccentricity of ellipse(x...

If `e_(1)` is the eccentricity of ellipse`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` and `e_(2)` is the eccentricity of `(x^(2))/(b^(2))+(y^(2))/(a^(2))=1` then

A

` e_(1)=e_(2)`

B

`e_(1) e_(2)=1`

C

` (1)/(e_(1)^(2))+(1)/(e_(2)^(2))=1`

D

`(e_(1))/(e_(2))=2`

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The correct Answer is:
A
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HIMALAYA PUBLICATION-ELLIPSE-QUESTION BANK
  1. Normal at one end of the latus rectum of the ellipse (x^(2))/(a^(2))+(...

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  2. Equation of the ellipse is (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with foci...

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  3. If e(1) is the eccentricity of ellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=...

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  4. If S(1) and S(2) are the foci of (x^(2))/(25)+(y^(2))/(16)=1 and Pis a...

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  5. C is the centre of the ellipse (x^(2))/(25)+(y^(2))/(16)=1 and S is on...

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  6. If the eccentricity of the ellipse is (2)/(3), then the ratio of the m...

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  7. The product of the perpendiculars from the foci of the ellipse (x^(2))...

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  8. If P is any point on the ellipse 16 x^(2)+25 y^(2)=400 then P S(1)+P S...

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  9. The equation (x^(2))/(10-a)+(y^(2))/(4-a)=1 represents an ellipse if

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  10. The equation of the director circle of the ellipse x^(2)+2y^(2)+2x-12y...

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  11. Equation of the auxilary circle of the ellipse 3 x^(2)+4 y^(2)+6 x+16 ...

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  12. Length of the latus rectum of the ellipse 2 x^(2)+y^(2)-8 x+2 y+7=0 is

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  13. The foci of the ellipse 25(x+1)^(2)+9(y+2)^(2)=225 are at

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  14. The locus of the point which moves such that sum of its distance from ...

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  15. If S(1) and S(2) are the foci of (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and...

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  16. If the tangents drawn from a point (1,2 sqrt(3)) to the ellipse (x^(2)...

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  17. If e(1) and e(2) are eccentricities of the ellipse (x^(2))/(18)+(y^(2)...

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  18. The tangents at the ends of the latus rectum L S(1) L^(prime) of the e...

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  19. The tangent to the ellipse (x^(2))/(25)+(y^(2))/(16)=1 at the end of t...

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  20. Area of the quadrilateral formed by the tangents at the ends of latus ...

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