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Question

If the abscissae and ordinates of two points P and Q are roots of the equations x2+2axb2=0
and x2+2pxq2=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
(xα)(xβ)+(yγ)(yδ)=0x2+y2(α+β)x(γ+δ)y+αβ+γδ=0x2+y2+2ax+2pyb2q2=0


Mathematics
RD Sharma
Standard XI

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