Pair of Tangents from an External Point

Pair of Tangents from an External Point

For circle:

$$S=0$$

and external point $$(x_1,y_1)$$, the pair of tangents is represented by:

$$T^2=SS_1$$

Terminology

- $$s$$ → Circle equation evaluated at variable point $$(x,y)$$.

- $$S_1$$ → Value of $$s$$ at $$(x_1,y_1)$$.

- $$t$$ → Polar expression obtained by replacing quadratic terms appropriately.

Usage

- Used to obtain the combined equation of the two tangents drawn from an external point.