# Find Equation of Tangent Line to Ellipse

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

We have standard equation of ellipse

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

Let be 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 .