Given equation of two intersecting circle’s S₁ = 0 & S₂ = 0. Equation of family of circles passing through the intersection point’s of S₁ = 0 & S₂ = 0 is ${\mathrm{S}}_1+{\mathrm{\lambda S}}_2=0$ , (where $\lambda \ne -1)$ Equation of common chord is S₁ – S₂ = 0

Equation of chord of contact for circle ${\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{gx}+2\mathrm{fy}+\mathrm{c}=0$ with respect to external point $\left({\mathrm{x}}_{\mathrm{p}},{\mathrm{y}}_1\right)\text{ is }{\mathrm{xx}}_1+{\mathrm{yy}}_1+\mathrm{g}\left(\mathrm{x}+{\mathrm{x}}_1\right)+\mathrm{f}\left(\mathrm{y}+{\mathrm{y}}_1\right)+\mathrm{c}=0$