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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
B
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