The length of the latus rectum of the parabola whose focus is $(3,3)$ and directrix is $3x - 4y - 2 = 0$ is . . . . . . units.

Find the equation of the parabola whose axis is parallel to the $y$-axis and which passes through the points $(0,4), (1,9)$ and $(4,5)$.

Let the locus of the mid-point of the chord through the origin $O$ of the parabola $y^{2}=4x$ be the curve $S$. Let $P$ be any point on $S$. Then the locus of the point,which internally divides $OP$ in the ratio $3:1$,is:

Let $A$ and $B$ be two distinct points on the parabola $y^2 = 4x$. If the axis of the parabola touches a circle of radius $r$ having $AB$ as its diameter,then the slope of the line joining $A$ and $B$ can be

Normals at $P$,$Q$,and $R$ are drawn to the parabola $y^2 = 4x$ which intersect at the point $(3, 0)$. Then,the triangle $\Delta PQR$ is:

Consider the parabola $y^2+2x+2y-3=0$ and match the items of List-$I$ with those of the List-$II$.

$A. \ 2x-5=0$	$I. \ \text{Vertex}$
$B. \ (\frac{3}{2}, -1)$	$II. \ \text{Focus}$
$C. \ y+1=0$	$III. \ \text{Equation of directrix}$
$D. \ (2, -1)$	$IV. \ \text{Equation of the axis}$
	$V. \ \text{Equation of the Latus rectum}$

The correct match is: