 The slopes of perpendicular lines have product −1, so if the equation of the curve is "y" = "f"("x") then slope of the normal line is
and it follows that the equation of the normal line at (X, Y) is
Similarly, if the equation of the curve has the form "f"("x", "y") = 0 then the equation of the normal line is given by

If the curve is given parametrically by
then the equation of the normal line is

The angle between two curves at a point where they intersect is defined as the angle between their tangent lines at that point.More specifically, two curves are said to be tangent at a point if they have the same tangent at a point, and orthogonal if their tangent lines are orthogonal.The formulas above fail when the point is a singular point.