If a hyperbola passes through the focus of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and its transverse and conjugate axes coincide with the major and minor axes of the ellipse, and the product of eccentricities is 1 , then
Select ALL correct options:
A
the equation of hyperbola is $\frac{x^2}{9}-\frac{y^2}{16}=1$
B
the equation of hyperbola is $\frac{x^2}{9}-\frac{y^2}{25}=1$
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