The equation of the ellipse is  and the point is .

Slope of the tangent is the derivative of the curve.

Consider .

Differentiate on each side with respect to .

.

Assume that the ellipse has the tangent at the point .

Slope of the tangent at .

.

Find the equation of the tangent at .

Point-slope form of line equation is .

Substitute  and  in point - slope form.

.

The above line passes through the point .

So it will satisfy the above tangent line equation.

The point  lies on ellipse.

Therefore, .

Substitute above result in .

.

Substitute  in .

 and .

Substitute values of  in .

If , then .

If , then .

Thus, the tangent points are  and .

Find the equation of the tangent line at .

Slope of the tangent line at :

.

Point - slope form of line equation is .

Substitute  and  in point - slope form.

Equation of the tangent to ellipse at  is .

Find the equation of the tangent line at .

Slope of the tangent line at :

.

Tangent at :

Point-slope form of line equation is .

Substitute  and  in point - slope form.

Equation of the tangent to ellipse at  is .

Tangent lines to ellipse are  and .