Definition:Line at Infinity

Definition
Let $\LL$ be a straight line embedded in a cartesian plane $\CC$ given in homogeneous Cartesian coordinates by the equation:


 * $l X + m Y + n Z = 0$

Let $l = m = 0$.

Then from Intersection of Straight Line in Homogeneous Cartesian Coordinates with Axes, $\LL$ intersects both the $x$-axis and the $y$-axis at the point at infinity.

Such a straight line cannot exist on $\CC$, so such an $\LL$ is known as the line at infinity.