If the abscissa and ordinates of two points `Pa n dQ` are the roots of the equations `x^2+2a x-b^2=0` and `x^2+2p x-q^2=0` , respectively, then find the equation of the circle with `P Q` as diameter.

Explanation

The abscissae of two points P and Q are the roots of `x^{2}+2 a x-b^{2} = 0 `


ordinates are the roots of` x^{2}+2 p x-q^{2}=0.`


Roots for quadratic equation `x^{2}+2 a x-b^{2}=0`


`Rightarrow x=frac{-2 a pm sqrt{(2a)^{2}-4(1)(-b^{2})}}{2(1)}`


`Rightarrow x=frac{-2 a pm sqrt{4(a^{2}+b^{2})}}{2} `


`Rightarrow x=-a pm sqrt{a^{2}+b^{2}} ldots (1)`


Roots for quadratic equation ` x^{2}+2 p x-q^{2}=0`


`Rightarrow x=frac{-2 p pm sqrt{(2 p)^{2}-4(1)(-q^{2})}}{2(1)}`


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