The foci of a hyperbola coincide with the foci of the ellipse `(x^2)/(25)+(y^2)/9=1.` Find the equation of the hyperbola, if its eccentricity is 2.

Explanation

To find the equation of the hyperbola whose foci coincide with the foci of the given ellipse \(\frac{x^2}{25} + \frac{y^2}{9} = 1\) and with an eccentricity of 2, we can follow these steps:

### Step 1: Identify the parameters of the ellipse
The given equation of the ellipse is:
\[ \frac{x^2}{25} + \frac{y^2}{9} = 1 \]
From this equation, we can identify:
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