Let S1:x2+y2+3x+2y+1=0 S2:x2+y2−x+6y+5=0 S3:x2+y2+5x−8y+15=0 Let (x,y) be the radical centre, then S1→S2=0 and S2−S3=0 ⇒4x−4y−4=0 and −6x+14y−10=0 ⇒x=y+1 and 3x−7y+5=0
⇒3(y+1)−7y+5=0⇒3y+3−7y+5=0
⇒−4y+8=0 ∴y=2 and x=2+1=3 Radical centre is (3,2).