# Find the Equation of the Tangent Line to the Ellipse

Find the equation of the tangent and normal to the ellipse at the point .

We have the standard equation of an ellipse

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

Let be 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 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 .