(a).

The ellipse is  and the point is .

Rewrite the function as .

Apply derivative on each side with respect to .

.

Slope of the tangent at point is the derivative of the function at that point.

The derivative of the function at .

Substitute and in .

.

Slope of the tangent at point is .

The general form of the equation is .

Substitute and  in the function .

Substitute and in the function .

The tangent line equation is .

(b).

 The functionn is and the point is

Rewrite the function as .

Apply derivative on each side with respect to .

Slope of the tangent at point is the derivative of the function at that point.

The derivative of the function at .

Substitute and in .

.

Slope of the tangent at point is .

The general form of the equation is .

Substitute and  in the function .

.

Substitute and in the function .

Substitute in the function then .

Substitute in the function .

The tangent line equation is .

(a) The tangent line equation is .

(b) The tangent line equation is .