Tangential Equation of A Point
A linear equation in line coordinates has the form al + bm + c = 0, where a, b and c are constants. Suppose (l, m) is a line that satisfies this equation. If c is not 0 then lx + my + 1 = 0, where x = a/c and y = b/c, so every line satisfying the original equation passes though the point (x, y). Conversely, any line through (x, y) satisfies the original equation, so al + bm + c = 0 is the equation of set of lines through (x, y). For a given point (x, y), the equation of the set of lines though it is lx + my + 1 = 0, so this may be defined as the tangential equation of the point. Similarly, for a point (x, y, z) given in homogeneous coordinates, then the equation of the point in homogeneous tangential coordinates is (lx, my, nz) = 0.
Read more about this topic: Line Coordinates
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