If the foci of the ellipse `(x^2)/(16)+(y^2)/(b^2)=1` and the hyperbola `(x^2)/(144)-(y^2)/(81)=1/(25)` coincide write the value of `b^2dot`

Explanation

To solve the problem, we need to find the value of \( b^2 \) such that the foci of the given ellipse and hyperbola coincide.

### Step-by-Step Solution:

1. **Identify the equations**:
- The equation of the ellipse is given by:
\[
\frac{x^2}{16} + \frac{y^2}{b^2} = 1
...