Find the equation of the circle passing through the points of intersection of the ellipses `(x^(2))/(16) + (y^(2))/(9) =1` and `(x^(2))/(9) + (y^(2))/(16) =1`.

Explanation

To find the equation of the circle that passes through the points of intersection of the given ellipses, we will follow these steps:

### Step 1: Write the equations of the ellipses
The equations of the ellipses are given as:
1. \(\frac{x^2}{16} + \frac{y^2}{9} = 1\)
2. \(\frac{x^2}{9} + \frac{y^2}{16} = 1\)

### Step 2: Multiply both equations to eliminate fractions
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