A term generically synonymous with perpendicular, which often refers specifically to a line that goes through a point P of a curve C and is perpendicular to the tangent to C at P. If a plane curve C has equation y = f(x), in rectangular coordinates the normal (line) to C at P(x₀,y₀) has slope −1/f^′(x₀), provided f^′(x₀) ≠ 0. The expression f^′(x₀) denotes the derivative of f(x), evaluated for x=x₀, and so the normal has equation y − y₀ = (−1/f^′(x₀)) (x − x₀). If curve C is not a plane curve, all normal lines of C at point P on C lie in a plane, the normal plane of C at P. For other uses of normal (for example, normal form of equation of a line or a plane)