The abscissae of the two points \( A \) and \( B \) are the roots of the equation \( x^{2}+2 a x...

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The abscissae of the two points \( A \) and \( B \) are the roots of the equation \( x^{2}+2 a x-b^{2}=0 \) and their ordinates are the roots of the equation \( x^{2}+2 p x-q^{2}=0 \). Find the equation of the circle with \( A B \) as diameter. Also, find its radius.
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