# Equation of Tangent and Normal to the Ellipse

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

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

Since the point lies on the given ellipse, 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 a tangent at the given point is

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

The slope of the normal at is

The equation of the normal at the point is

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