The length of the chord $y=\sqrt{3}x-2\sqrt{3}$ intercepted by the parabola $y^2=4(x-1)$ is

Identify the following statements for true/false (T/F) in order
$S1:$The tangents at the extremities of a focal chord of a parabola are perpendicular
$S2:$ The tangents at the extremities of a focal chord of a parabola are parallel
$S3:$The tangents at the extremities of a focal chord of a parabola intersect on the directrix

$\mathrm{S}4$ : The tangents at the extremities of a focal chord of a parabola intersect at the vertex