# Equation of Tangent and Normal to Ellipse

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

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

Since the point lies on the given ellipse, so it must satisfy equation (i), we have

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

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

Equation of tangent at the given point is

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

Slope of the normal at is

Equation of normal at the point is

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