JEE Math Practice Question

A hyperbola passes through the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is :

1. A.$${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$
2. B.$${{{x^2}} \over 9} - {{{y^2}} \over 16} = 1$$
3. C.$${{{x^2}} \over 9} - {{{y^2}} \over 25} = 1$$
4. D.x2 $$-$$ y2 = 9