The Concept

Let y =f(x) be a given curve and P(x,y) and  Q(x + δx ,y + δy)be two neighbouring points on it.

When Q → P, i.e.,  δx → 0 line PQ becomes tangent to the curve y = f (x) at point P. We also know that

Normal at P(x, y)

The normal at P (x, y) is perpendicular to tangent (2) therefore, its slope is

Hence, its equation is