# Equations of Tangent and Normal to the Parabola

The equations of tangent and normal to the parabola at the point are and respectively.

Consider that the standard equation of a parabola with vertex at origin can be written as

Since the point lies on the given parabola, it must satisfy equation (i). So we have

Now differentiating equation (i) on both sides with respect to , we have

If represents the slope of the tangent at the given point , then

The equation of the tangent at the given point is

This is the equation of the tangent to the given parabola at .

The slope of normal at is

The equation of normal at the point is

This is the equation of normal to the given parabola at .