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If e(1) and e(2) represent the eccentric...

If `e_(1)` and `e_(2)` represent the eccentricity of the curves `6x^(2) - 9y^(2) = 144` and `9x^(2) - 16y^(2) = 144` respectively . Then `(1)/(e_(1)^(2)) + (1)/(e_(2)^(2))` is equal to

A

`e_1^2-e_2^2=1`

B

`e_1^2-e_2^2lt3`

C

`e_1^2-e_2^2=3`

D

`e_1^2-e_2^2gt3`

Text Solution

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The correct Answer is:
B
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ARIHANT MATHS-HYPERBOLA-Exercise For Session 1
  1. The eccentricity of the conic represented by x^2-y^2-4x+4y+16=0 is 1 (...

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  2. If e(1) and e(2) represent the eccentricity of the curves 6x^(2) - 9y^...

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  3. The transverse axis of a hyperbola is of length 2a and a vertex divide...

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  4. The eccentricity of the hyperbola whose latuscrectum is 8 and conjugat...

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  5. The straight line x+y=sqrt2p will touch the hyperbola 4x^2-9y^2=36 i...

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  6. The equation of the tangent parallel to y-x+5=0" drawan to "(x^(2))/(3...

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  7. If e and e' are the eccentricities of the hyperbola x^2/a^2-y^2/b^2=1...

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  8. If e and e' are the eccentricities of the ellipse 5x^(2) + 9 y^(2) = ...

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  9. The equation (x^(2))/(10-lambda)+(y^(2))/(6-lambda)=1 represents

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  10. Find the centre, eccentricity, foci and directrices of the hyperbola :...

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  11. For hyperbola x^2sec^2alpha-ycos e c^2alpha=1, which of the following ...

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  12. If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola ...

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  13. Find the standard equation of hyperbola in each of the following cases...

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  14. Find the equation of the hyperbola whose foaci are (0, 5) and (-2, 5) ...

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  15. Prove that the straight lines x/a-y/b =m and x/a+y/b=1/m, where a and ...

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  16. Find the centre, eccentricity and length of axes of the hyperbola 3x^...

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  17. The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=...

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  18. If the line y=3x+lambda touches the hyperbola 9x^(2)-5y^(2)=45, then l...

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  19. Find the equation of tangents to the curve 4x^2-9y^2=1 which are paral...

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