If the line $y = 4 + kx$,$k > 0$,is the tangent to the parabola $y = x - x^{2}$ at the point $P$ and $V$ is the vertex of the parabola,then the slope of the line through $P$ and $V$ is

If the straight line $y=mx+c$ is parallel to the axis of the parabola $y^2=lx$ and intersects the parabola at $\left(\frac{c^2}{8}, c\right)$,then the length of the latus rectum is

The parabola with directrix $x+2y-1=0$ and focus $(1,0)$ is

The latus rectum of a parabola whose focal chord $PSQ$ is such that $SP = 3$ and $SQ = 2$ is given by

Let $E$ denote the parabola $y^2=8x$. Let $P=(-2,4)$,and let $Q$ and $Q^{\prime}$ be two distinct points on $E$ such that the lines $PQ$ and $PQ^{\prime}$ are tangents to $E$. Let $F$ be the focus of $E$. Then which of the following statements is (are) $TRUE$?
$(A)$ The triangle $PFQ$ is a right-angled triangle
$(B)$ The triangle $QPQ^{\prime}$ is a right-angled triangle
$(C)$ The distance between $P$ and $F$ is $5\sqrt{2}$
$(D)$ $F$ lies on the line joining $Q$ and $Q^{\prime}$

If $2x + 3y + 12 = 0$ and $x - y + 4\lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $\lambda$ is equal to