The longest distance of the point $(a,0)$ from the curve $2x^2+y^2=2x$ is :

Question

$$\begin {array} {1 1} (1)\;1+a & \quad (2)\;|1-a| \\ (3)\;\sqrt {1-2a+2a^2} & \quad (4)\;\sqrt {1-2a+3a^2} \end {array}$$