The equation of the directrix of the parabola $y^2+4y+4x+2=0$ is

The normal at the point $(bt_1^2, 2bt_1)$ on the parabola $y^2 = 4bx$ meets the parabola again at the point $(bt_2^2, 2bt_2)$. Then:

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 $Q^{\prime}$

The line $x + y = 6$ is a normal to the parabola $y^2 = 8x$ at the point

The condition that the parabolas $y^2 = 4ax$ and $y^2 = 4c(x - b)$ have a common normal other than the $x$-axis ($a, b, c$ being distinct positive real numbers) is

The vertex of the parabola $3x - 2y^2 - 4y + 7 = 0$ is