The abscissa of the two points A and B are the roots of the equation `x^2+2a x-b^2=0` and their ordinates are the roots of the equation `x^2+2p x-q^2=0.` Find the equation of the circle with AB as diameter. Also, find its radius.

Explanation

To find the equation of the circle with points A and B as the diameter and to determine its radius, we will follow these steps:

### Step 1: Identify the Roots of the Given Equations
The abscissa (x-coordinates) of points A and B are the roots of the equation:
\[ x^2 + 2ax - b^2 = 0 \]
The roots of this equation can be found using the quadratic formula:
\[ x = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A} \]
Here, \( A = 1, B = 2a, C = -b^2 \).
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