The line perpendicular to the tangent line to a curve at the point of tangency is called the "normal line" to the curve at that point. 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

Intuitive description
Tangent line to a curve
Multiple tangents at a point
Normal line to a curve