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 .

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Assume that the ellipse has the tangent at the point .

Slope of the tangent at .

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Find the equation of the tangent at .

Point-slope form of line equation is .

Substitute and in point - slope form.

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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 .

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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 .