PQ is a chord of the circle x2+y2−2x−8=0 whose midpoint is (2, 2). The circle passing through P, Q and (1, 2) is

The equation of the chord of the circle x2+y2−2x−8=0 having (2, 2) as its mid-point is2x+2y−(x+2)−8=4+4−4−8                     [Using: S′=T ] ⇒x+2y−6=0 The equation of a circle passing through P and Q isx2+y2−2x−8+λ(x+2y−6)=0                       ... (i)It passes through (1, 2).∴ 1+4−2−8+λ(1+4−6)=0⇒λ=−5Putting the value of λ in (i), we obtainx2+y2−7x−10y+22=0as the equation of the required circle.