Definition:Tangential Equation of Circle

Definition
Let $\CC$ be a circle embedded in the Cartesian plane of radius $r$ with its center located at the origin.

Let $\LL$ be a straight line in the plane of $\CC$ whose equation is given by:
 * $(1): \quad l x + m y + n = 0$

such that $l \ne 0$.

Then the equation:
 * $\paren {l^2 + m^2} r^2 = n^2$

is known as the tangency equation of $\CC$.

Also see

 * Condition of Tangency to Circle whose Center is Origin, which justifies the definition