If $x + y = k$ is a normal to the parabola $y^2 = 12x$,then what is the value of $k$?

Let $P(x, y)$ be a variable point on the parabola $y = 4x^2 + 1$. Let $Q(c, c)$ be the foot of the perpendicular drawn from $P$ to the line $y = x$. If $R(h, k)$ is the mid-point of $PQ$,then the locus of $R$ is:

If the line $lx + my + n = 0$ is tangent to the parabola $y^{2} = 4ax$,then

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:

What is the angle subtended by the latus rectum of the parabola $y^2 = ax$ at its vertex?

Which of the following lines is a normal to the parabola $y^2 = 16x$?