A particle is moving in the $x y$-plane along a curve $C$ passing through the point $( 3,3 )$. The tangent to the curve $C$ at the point $P$ meets the $x$-axis at $Q$. If the $y$-axis bisects the segment $P Q$, then $C$ is a parabola with\\
(1) length of latus rectum 3\\
(2) length of latus rectum 6\\
(3) focus $\left( \frac { 4 } { 3 } , 0 \right)$\\
(4) focus $\left( 0 , \frac { 3 } { 3 } \right)$