The sides of the rectangle of greatest area that can be inscribed in the ellipse $x^2+4y^2=64$ are:

Question

$$\begin {array} {1 1} (a)\;(6 \sqrt 2, 4 \sqrt 2) & \quad (b)\;(8 \sqrt 2,4 \sqrt 2) \\ (c)\;(8 \sqrt 2,8 \sqrt 2) & \quad (d)\;(16 \sqrt 2,4 \sqrt 2)\end {array}$$