JEE Advance - Mathematics (2006 - No. 23)
Let a hyperbola passes through the focus of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$$. The transverse and conjugate axes of this hyperbola coincide with the major and minor axes of the given ellipse, also the produced of eccentricities of given ellipse and hyperbola is $$1$$, then
the equation of hyperbola is $${{{x^2}} \over 9} + {{{y^2}} \over {16}} = 1$$
the equation of hyperbola is $${{{x^2}} \over 9} + {{{y^2}} \over {25}} = 1$$
focus of hyperbola is $$(5, 0)$$
vertex of hyperbola is $$\left( {5\sqrt 3 ,0} \right)$$