The transformed equation of $3x^2+3y^2,2xy=2$ when the coordinate axes are rotated through an angle of $45^{\circ}$ is

Question

\[\begin {array} {1 1} (1)\;x^2+2y^2=1 & \quad (2)\;2x^2+y^2=1 \\ (3)\;x^2+y^2=1 & \quad (4)\;x^2+3y^2=1 \end {array}\]