(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 .

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 .