The transformed equation of $x^2+y^2=r^2$ when the axes are rotated through an angle $36^{\circ}$ is :

Question

\[\begin {array} {1 1} (1)\;\sqrt 5X^2-4XY+Y^2=r^2 & \quad (2)\;X^2+2XY-\sqrt 5 Y^2=r^2 \\ (3)\;X^2-Y^2=r^2 & \quad (4)\;X^2+Y^2=r^2 \end {array}\]