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 \( b^2 \) given that the foci of the ellipse and hyperbola coincide.

### Step 1: Analyze the hyperbola
The equation of the hyperbola is given as:
\[ \frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25} \]
To convert this into standard form, we multiply through by 25:
...