If `a` hyperbola passes through the foci of the ellipse `(x^2)/(25)+(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 `(x^2)/9-(y^2)/(16)=1` b. the equation of hyperbola is `(x^2)/9-(y^2)/(25)=1` c. focus of hyperbola is (5, 0) d. focus of hyperbola is `(5sqrt(3),0)`

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Identify the given ellipse
The equation of the ellipse is given as:
\[ \frac{x^2}{25} + \frac{y^2}{16} = 1 \]
From this equation, we can identify:
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