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If e(1) is the eccentricity of the ellip...

If `e_(1)` is the eccentricity of the ellipse `x^(2)/16+y^(2)/25=1` and `e_(2)` is the eccentricity of a hyperbola passing through the foci of the given ellipse and `e_(1)e_(2)=1`, then the equation of such a hyperbola among the following is

A

`x^(2)/(16)+y^(2)/(25)=1`

B

`(x^(2))/(16)-y^(2)/9=-1`

C

`x^(2)/9-y^(2)/(25)=1`

D

`x^(2)/(16)-y^(2)/9=1`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-HYPERBOLA-Exercise -II
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  2. The transverse axis of a hyperbola is of length 2a and a verlex divide...

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  3. If e(1) is the eccentricity of the ellipse x^(2)/16+y^(2)/25=1 and e(2...

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  4. The equation (x^(2))/(7-K) +(y^(2))/(5-K)=1 represents a hyperbola if

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  5. If the foci of the ellips (x^(2))/( 25)+ ( y^(2))/( 16) =1 and the hy...

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  6. The foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbla (x^2...

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  7. Statement-I : If P,Q,R,S are the ends of latus recta of the hyperbola ...

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  8. The eccentricity of the hyperbola 4x^(2)-9y^(2)=2ax +b^(2) is

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  9. The eccentricity of x^(2)/9-y^(2)/(16)=1 is

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  10. If (5,12), (24,7) are the foci of the hyperbola passing through origin...

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  11. If the ecentricity of a hyperbola is sqrt3 then the ecentricity of its...

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  12. If e and e^1 are the eccentricities of the ellipse 5x^(2)+9y^(2)=45 an...

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  13. If the equation (10x-5)^(2)+(10y 4)^(2)=lambda^(2) (3x+4y-1)^(2) repre...

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  14. Statement-I: The number of integral values of K for which the equation...

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  15. The equation of the director circle of x^(2)//12-y^(2)//8=1 is

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  16. If the tangents drawn from a point on the hyperola x^(2)-y^(2)=a^(2)-b...

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  17. Equation of one of the tangents passing through (2, 8) to the hyperbol...

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  18. The locus of the point of Interection of two tangents to the hyperbola...

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  19. Locus of P such that the chord of contact of P with respect to y^2= 4a...

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