The area (in sq. units) of the smaller of the two circles that touch the parabola, $y ^ { 2 } = 4 x$ at the point $( 1,2 )$ and the $x$-axis is\\
(1) $8 \pi ( 3 - 2 \sqrt { 2 } )$\\
(2) $8 \pi ( 2 - \sqrt { 2 } )$\\
(3) $4 \pi ( 3 + \sqrt { 2 } )$\\
(4) $4 \pi ( 2 - \sqrt { 2 } )$