Tangent and Normal Formulas
The 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 ,

The equation of the tangent at a point is

The 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