(a) If the abscissa and ordinates of two points P and Q are the roots of the equations x\power{2}+2ax-b\power{2}=0 and x\power{2}+2px-q\power{2}=0 respectively, then find the equation of the circle with PQ as diameter. (b)Find the equation of the circle which passes through (1, 0) and (0, 1)  and has its radius as small as possible.

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A: