The normal to the parabola ${y^2 = 8x}$ at the point $(2, 4)$ meets the parabola again at the point

Consider the parabola $y^2=4x$. Let $S$ be the focus of the parabola. $A$ pair of tangents drawn to the parabola from the point $P=(-2,1)$ meet the parabola at $P_1$ and $P_2$. Let $Q_1$ and $Q_2$ be points on the lines $SP_1$ and $SP_2$ respectively such that $PQ_1$ is perpendicular to $SP_1$ and $PQ_2$ is perpendicular to $SP_2$. Then,which of the following is/are $TRUE$?
$(A)$ $SQ_1=2$
$(B)$ $Q_1Q_2=\frac{3\sqrt{10}}{5}$
$(C)$ $PQ_1=3$
$(D)$ $SQ_2=1$

If $t_1$ and $t_2$ are the parameters of the end points of a focal chord for the parabola $y^2 = 4ax$, then which one is true?

Let $P : y^{2} = 4ax, a > 0$ be a parabola with focus $S$. Let the tangents to the parabola $P$ that make an angle of $\frac{\pi}{4}$ with the line $y = 3x + 5$ touch the parabola $P$ at $A$ and $B$. Then the value of $a$ for which $A, B$ and $S$ are collinear is:

If two perpendicular rays from the focus of the parabolic surface $y^2 = 4x$ are incident at points $A(t_1^2, 2t_1)$ and $B(t_2^2, 2t_2)$ such that $t_1t_2 = -1$,then the distance between the reflected rays is -

Tangents are drawn at three points $P(t_1), Q(t_2), R(t_3)$ on the parabola $y^2 = x$. Let these tangents intersect each other at the points $L, M, N$. If $t_1 = 2, t_2 = -4, t_3 = 6$,then the area of the triangle $LMN$ is