The slope of the chord of the parabola $y^2 = 4ax$ which passes through the origin and is normal at one of its endpoints is:

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 $Q^{\prime}$

$A = (-2, 0)$ and $P$ is a point on the parabola $y^2 = 8x$. If $Q$ bisects $\overline{AP}$ and the locus of $Q$ is a parabola,then its focus is

The length of the latus rectum of the conic $25[(x-2)^2+(y-3)^2]=(3x-4y+7)^2$ is

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

The line $lx + my + n = 0$ will touch the parabola $y^2 = 4ax$,if