The tangent drawn at any point $P$ to the parabola ${y^2} = 4ax$ meets the directrix at the point $K$. Then the angle which $KP$ subtends at its focus is ............. $^\circ$.

$A$ ray of light moving parallel to the $x$-axis gets reflected from a parabolic mirror whose equation is $(y - 2)^2 = 4(x + 1)$. After reflection,the ray must pass through the point:

Let $P$ be the point $(1, 0)$ and $Q$ be a point on the parabola $y^2 = 8x$. Find the locus of the midpoint of $PQ$.

If the line $x + y = 1$ is a normal to the parabola $y^2 = kx$,then find the value of $k$. (in $/3$)

For the parabola $y=x^2-3x+2$,match the items in List-$I$ to that of the items in List-$II$. $S$ is a focus,$Z$ is the intersection of the axis and the directrix,$P$ is one end point of the latus rectum,$Q$ is the point on the parabola at which the tangent is parallel to the $X$-axis.

$A$. $P$	$I$. $(2,0)$
$B$. $Q$	$II$. $(\frac{3}{2}, -\frac{1}{4})$
$C$. $S$	$III$. $(\frac{3}{2}, 0)$
$D$. $Z$	$IV$. $(\frac{3}{2}, -\frac{1}{2})$
	$V$. $(0, \frac{3}{2})$

If $a \ne 0$ and the line $2bx + 3cy + 4d = 0$ passes through the points of intersection of the parabolas $y^2 = 4ax$ and $x^2 = 4ay$,then