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Let a hyperbola passes through the focus...

Let a hyperbola passes through the focus of the ellipse `(x^(2))/(25)+(y^(2))/(16)=1`. The transverse and conjugate axes of this hyperbola coincide with the major and minor axis of the given ellipse. Also, the product of the eccentricities of the given ellipse and hyperbola is 1. Then,

A

the equation of hyperbola is `(x^(2))/(9)-(y^(2))/(16)=1`

B

the equation of hyperbola is `(x^(2))/(9)-(y^(2))/(25)=1`

C

focus of hyperbola is `(5, 0)`

D

vertex of hyperbola is `(5sqrt(3), 0)`

Text Solution

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The correct Answer is:
A, C
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