Chord of Contact of a Conic

For a conic $$S\equiv ax^2+2hxy+by^2+2gx+2fy+c=0$$, the chord of contact from point $$(x_1,y_1)$$ is given by $$T=0$$, where

$$T\equiv a\,x\,x_1+h(x\,y_1+x_1\,y)+b\,y\,y_1+g(x+x_1)+f(y+y_1)+c=0.$$

In particular, for the circle $$x^2+y^2=r^2$$, the chord of contact from $$(x_1,y_1)$$ is

$$xx_1+yy_1=r^2.$$