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==Equations==
Let {{math|''f''(''x'', ''y'', ''z'') {{=}} 0}} be the equation of a curve in [[homogeneous coordinates]]. Let {{math|''Xx'' + ''Yy'' + ''Zz'' {{=}} 0}} be the equation of a line, with {{math|(''X'', ''Y'', ''Z'')}} being designated its [[line coordinates]]. The condition that the line is tangent to the curve can be expressed in the form {{math|''F''(''X'', ''Y'', ''Z'') {{=}} 0}} which is the tangential equation of the curve.
Let {{math|(''p'', ''q'', ''r'')}} be the point on the curve, then the equation of the tangent at this point is given by
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