Let \( O \) be the vertex of the parabola \( y^{2}=4x \) and its chords \( OP \) and \( OQ \) are perpendicular to each other. If the locus of the mid-point of the line segment \( PQ \) is a conic \( C \), then the length of its latus rectum is:
\( 1 \)
\( 2 \)
\( 4 \)
\( 8 \)
