Normal to a Curve

What is Normal to a Curve?

The straight line through a point on a curve that is perpendicular to the tangent at that point. If the tangent has non-zero gradient m, the normal has gradient equal to minus one over m, because the product of the gradients of two perpendicular non-vertical lines is minus one. Where the tangent is horizontal the normal is vertical and has the equation x equals a rather than a gradient; where the tangent is vertical the normal is horizontal. The normal is found from the same derivative as the tangent, so no new differentiation is required once the gradient at the point is known.

This definition is part of the Calculus chapter in Cambridge O Level Additional Mathematics.

Concepts related to Normal to a Curve

• negative reciprocal
• tangent gradient
• point–gradient form