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If a hyperbola passes through a focus of the ellipse `(x^(2))/(25)+(y^(2))/(16)`=1 and its transverse and conjugate axes coincide with major and minor axes of the ellipse and the product of their eccentricities is 1, then the equation of hyperbola is

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
A
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