Tangent and Normal Formulas
Formulas of Tangent and Normal to any curve at a given point are listed below:

is the slope of the tangent to the curve at the point

In a plane curve ,

Equation of the tangent at a point is

Equation of the normal at a point is

Consider that a curve is defined by , and is the length of the perpendicular from to the tangent at the point of the curve , then