If the segment of the parabola $y^2 = 4ax$ intercepted by its directrix subtends an angle $\theta$ at its focus,then $\theta = \dots$

Let $P$ and $Q$ be points on the parabola $y^{2}=4x$ such that the line segment $PQ$ subtends a right angle at the vertex. If $PQ$ intersects the axis of the parabola at $R$, then the distance of the vertex from $R$ is

If the line $x - 1 = 0$ is the directrix of the parabola $y^2 - kx + 8 = 0$,then what is one value of $k$?

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4x$ is

The condition that the line $ax + by + c = 0$ is tangent to the parabola $y^2 = 4ax$ is:

Let $A_1, B_1, C_1$ be three points in the $xy$-plane. Suppose that the lines $A_1 C_1$ and $B_1 C_1$ are tangents to the curve $y^2=8x$ at $A_1$ and $B_1$,respectively. If $O=(0,0)$ and $C_1=(-4,0)$,then which of the following statement$(s)$ is (are) $TRUE$?
$(A)$ The length of the line segment $OA_1$ is $4\sqrt{3}$
$(B)$ The length of the line segment $A_1 B_1$ is $16$
$(C)$ The orthocenter of the triangle $A_1 B_1 C_1$ is $(0,0)$
$(D)$ The orthocenter of the triangle $A_1 B_1 C_1$ is $(1,0)$