If $a$ hyperbola passes through the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of a. hyperbola is $\frac{x^2}{9}-\frac{y^2}{16}=1$ b. the equation of hyperbola is $\frac{x^2}{9}-\frac{y^2}{25}=1$ c. focus of hyperbola is (5, 0) d. focus of hyperbola is $\left(5\sqrt{3},0\right)$

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