In polar coordinates 4x² + y² = 4 then using dividing by 4 gives

x² + y²/4 = 1

ie x² + (y/2)² = 1

x=cos(theta) , y=2sin (theta)

satisfies the relationship and is the polar coordinate reprentation of the ellipse, and the ellipse is traced out by varing theta from 0 to 2Pi, I do not understand what you mean by the rest of the question.

x² + y²/4 = 1

ie x² + (y/2)² = 1

x=cos(theta) , y=2sin (theta)

satisfies the relationship and is the polar coordinate reprentation of the ellipse, and the ellipse is traced out by varing theta from 0 to 2Pi, I do not understand what you mean by the rest of the question.