The equation of the latus rectum of the parabola represented by the equation ${y^2} + 2Ax + 2By + C = 0$ is

Find the equations of the tangent and normal to the parabola $y^{2}=4ax$ at the point $(at^{2}, 2at)$.

If the parabola $y^2 = 4ax$ passes through the point $(-3, 2)$,then the length of its latus rectum is

If the line $y = -x + k$ is normal to the curve $y^2 = 16x$,then $k$ is

$A$ line $L: y=mx+3$ meets the $y$-axis at $E(0,3)$ and the arc of the parabola $y^2=16x, 0 \leq y \leq 6$ at the point $F(x_0, y_0)$. The tangent to the parabola at $F(x_0, y_0)$ intersects the $y$-axis at $G(0, y_1)$. The slope $m$ of the line $L$ is chosen such that the area of the triangle $EFG$ has a local maximum.
Match List $I$ with List $II$ and select the correct answer using the code given below the lists:

List $I$	List $II$
$P. \quad m=$	$1. \quad 1/2$
$Q. \quad \text{Maximum area of } \triangle EFG \text{ is}$	$2. \quad 4$
$R. \quad y_0=$	$3. \quad 2$
$S. \quad y_1=$	$4. \quad 1$

Codes: $P \quad Q \quad R \quad S$

The equations $x = \frac{t}{4}$ and $y = \frac{t^2}{4}$ represent: