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 solve the problem step by step, we will follow the instructions given in the video transcript and elaborate on each step for clarity.

### 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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