IIT-JEE 2006 | Hyperbola Question 18 | Mathematics

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IIT-JEE 2006

MCQ (More than One Correct Answer)

+5

-1.25

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

A

the equation of hyperbola is $${{{x^2}} \over 9} + {{{y^2}} \over {16}} = 1$$

B

the equation of hyperbola is $${{{x^2}} \over 9} + {{{y^2}} \over {25}} = 1$$

C

focus of hyperbola is $$(5, 0)$$

D

vertex of hyperbola is $$\left( {5\sqrt 3 ,0} \right)$$