S≡x2+y2+αx+6y=0 S′≡x2+y2+2αx+αy+6=0 S′′≡x2+y2+6αx−αy+3=0 ‌ Radical axis are ‌ S−S′=−αx+(6−α)y−6=0 S−S′′=−5αx+(6+α)y−3=0 S′−S′′=−4αx+2αy+3=0 Radical centre is point of cencurrence of three radical axis ∴‌‌(0,‌
3
4
)‌ satisfies ‌S−S′=0 ⇒‌‌(6−α)‌
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−6=0⇒6−α=8⇒α=−2 ∴‌‌S′=x2+y2−4x−2y+6=0 ‌ Centre ‌=(2,1) ∴‌ Required distance ‌ ‌‌=√(2−0)2+(1−‌