The circles x² + y² + x + y = 0 and x² + y² + x - y = 0 intersect at an angle?

If S =  x² + y² + 2g₁x + 2f₁y + c₁ = 0 

and S“ ≡ x² + y² + 2g₂x + 2f₂y + c₂ = 0
$$\begin{gathered} \mathrm{then} \mathrm{angle} \mathrm{between} \mathrm{them} \mathrm{is} \mathrm{same} \mathrm{as} \mathrm{angle} \mathrm{between} \mathrm{their} \mathrm{tangent} \mathrm{and} \mathrm{formula} \\ \mathrm{is} \\ \mathrm{cos\theta }=\frac{2\left({\mathrm{g}}_1{\mathrm{g}}_2+{\mathrm{f}}_1{\mathrm{f}}_2\right)-{\mathrm{c}}_1-{\mathrm{c}}_2}{\sqrt{{{\mathrm{g}}_1}^2+{{\mathrm{f}}_1}^2-{\mathrm{c}}_1}\times \sqrt{{{\mathrm{g}}_2}^2+{{\mathrm{f}}_2}^2-{\mathrm{c}}_2}} \\ =\frac{2\left({\displaystyle \frac{1}{2}}\times {\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}\times \left({\displaystyle \frac{-1}{2}}\right)\right)-0}{\sqrt{{{\mathrm{g}}_1}^2+{{\mathrm{f}}_1}^2-{\mathrm{c}}_1}\times \sqrt{{{\mathrm{g}}_2}^2+{{\mathrm{f}}_2}^2-{\mathrm{c}}_2}} \\ =0 \\ \mathrm{so} \mathrm{cos\theta }=0 = \cos 90 \\ \mathrm{so} \mathrm{\theta }=90 \mathrm{and} \mathrm{hence} \mathrm{they} \mathrm{are} \mathrm{at} \mathrm{right} \mathrm{angle} \end{gathered}$$