The length of the latus rectum of the parabola ${y^2} = 5x + 4y + 1$ is

Which of the following points lie on the parabola $x^2 = 4ay$?

The equation of a parabola which passes through the intersection points of the straight line $x + y = 0$ and the circle $x^2 + y^2 + 4y = 0$ 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: $P \quad Q \quad R \quad S$

If a double ordinate of the parabola $y^2 = 4ax$ has a length of $8a$,then the angle between the lines joining the vertex of the parabola to the ends of this double ordinate is ............... $^\circ$.

If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2 = 4ax$,then the length of the semi-latus rectum is: