We have, equation of circles S1:x2+y2−4x−6y+k=0 and S2:x2+y2+8x−4y+11=0 Let C1,C2 are centres of circles and r1,r2 are radius of circles S1 and S2 respectively. ∴‌‌C1=(2,3),C2=(−4,2)
r1=√4+9−K=√13−x,r2=√16+4−11=3
Now, angle between circles is given by cos‌θ=‌