It is given that the circles x2+y2−2x−2y+k=0 and x2+y2+4x+6y+4=0 Touches each other externally, so c1c2=r1+r2 Where, c1(1,1),c2(−2,−3) and r1=√2−k,r2=3 So, √9+16=√2−k+3 √9+16=√2−k+3
⇒2=√2−k⇒4=2−k⇒k=−2
The point of contact P of two circles, divides the line joining centres c1 and c2 in the ratio r1:r2.