(a)

The ellipse is  and the point is .

Differentiate the equation with respect to .

Derivative of constant is zero.

Apply formula : .

Apply power rule of derivatives : .

Substitute the point  in above equation.

This is the slope of tangent to the ellipse at the point .

Slope of the tangent line is .

Point slope form of line equation is .

Substitute  and  in the above equation.

The tangent line equation is 

(b)

The ellipse is  and the point is .

Differentiate the equation with respect to .

Apply formula : .

Derivative of constant is zero.

Apply power rule of derivatives : .

Substitute the point  in above equation.

.

This is the slope of tangent to the ellipse at the point .

Slope of the tangent line is .

Point slope form of line equation is .

Substitute  and  in the above equation.

Divide each side by .

The tangent line equation is .

a) The tangent line equation is

b) The tangent line to the ellipse at is .