Here S ≡ x2 +y2 –4x+6y+11= 0 and S′ = x2 +y2 –2x+8y+13 =0
The centre of these circles are C1 (2,–3) and C2 (1,–4) respectively.
The radius of these circles are r1 = \(\sqrt{4+9-11}=\sqrt{2}\)
and r2 = \(\sqrt{1+16-13}=2\)
Distance between the centres C1 and C2 = d = \(\sqrt{1^2+1^2}=\sqrt{2}\)
Angle between two circle is cosθ = \(\left|\frac{r_1^2+r_2^2-(c_1c_2)^2}{2r_1r_2}\right|= \left|\frac{2+4-2}{2\times2\times\sqrt{2}}\right|=\frac{1}{\sqrt{2}}\)
=cos π/4
\(\therefore\)θ = π/4
