Let a hyperbola passes through the focus of the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \...

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Let a hyperbola passes through the focus of the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \). The transverse and conjugate axes of this hyperbola coincide with the major and minor axes of the given ellipse. Also, the product of the eccentricities of the given ellipse and hyperbola is 1 . Then
(a) The equation of the hyperbola is \( \frac{x^{2}}{9}-\frac{y^{2}}{16}=1 \)
(b) Ecentricity of the hyperbola is \( \frac{5}{3} \)
(c) The focus of the hyperbola is \( (5,0) \)
(d) The focus of the hyperbola is \( (5 \sqrt{3}, 0) \)
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