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Line 7: ==Equations== Let {{math\|''f''(''x'', ''y'', ''z'') {{=}} 0}} be the equation of a curve in [[homogeneous coordinates]] on the [[projective plane]]. Let {{math\|''Xx'' + ''Yy'' + ''Zz'' {{=}} 0}} be the equation of a line, with {{math\|(''X'', ''Y'', ''Z'')}} being designated its [[line coordinates]]~~<nowiki/>~~ in a dual projective plane. 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. At a point {{math\|(''p'', ''q'', ''r'')}} on the curve, the tangent is given by

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