Given x1,x2 are the roots of the equation x2+2x−3=0 ⇒x2+3x−x−3=0 ⇒x(x+3)−1(x+3)=0 ⇒(x−1)(x+3)=0 ⇒x1=−3,x2=1 and y1,y2 are the roots of the equation y2+4y−12=0 ⇒y2+6y−2y−12=0 ⇒y(y+6)−2(y+6)=0 ⇒(y−2)(y+6)=0 ⇒y1=−6,y2=2 ∴ Points are P(−3,−6) and Q(1,2). Since, P and Q are the end points of a diameter. ∴ Centre = mid point of PQ =(