 For algebraic curves, computations may be simplified somewhat by converting to homogeneous coordinates.Specifically, let the homogeneous equation of the curve be "g"("x", "y", "z") = 0 where "g" is a homogeneous function of degree "n".Then, if ("X", "Y", "Z") lies on the curve, Euler's theorem implies
formula_19
It follows that the homogeneous equation of the tangent line is
The equation of the tangent line in Cartesian coordinates can be found by setting "z"=1 in this equation.