If a hyperbola passes through the foci 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 respectively,and the product of their eccentricities is $1$,then:
- AThe focus of the hyperbola is $(5, 0)$.
- BThe focus of the hyperbola is $(5\sqrt{3}, 0)$.
- CThe equation of the hyperbola is $\frac{x^2}{9} - \frac{y^2}{25} = 1$.
- DThe equation of the hyperbola is $\frac{x^2}{9} - \frac{y^2}{16} = 1$.
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