The correct option is C 45o
S1:x2+y2−4x+6y+11=0
⇒C1(2,−3), r1=√2
S2:x2+y2−2x+8y+13=0
⇒C2(1,−4), r2=2
Distance between centres
d=|C1C2|
d=√(2−1)2+(−3+4)2=√2
If angle between the circles is θ, then
cosθ=(r21+r22−d22r1r2)
⇒cosθ=(2+4−22×√2×2)=1√2
⇒θ=45∘.