Question

# If the abscissae and ordinates of two points P and Q are roots of the equations x2+2ax−b2=0 and x2+2px−q2=0 respectively,  then write the equation of the circle with PQ as diameter.

Solution

## Let α,β and r, δ  are the roots of the first and second given equation,  so α+β=—2a,αβ=−b2γ+δ=−2p,γδ=−q2 Coordinates of P and Q are (α,γ) and (β,δ) respectively  The equation of circle on PQ as diameter is (x−α)(x−β)+(y−γ)(y−δ)=0x2+y2−(α+β)x−(γ+δ)y+αβ+γδ=0x2+y2+2ax+2py−b2−q2=0 MathematicsRD SharmaStandard XI

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