If the focus of a parabola is $(3, -4)$ and its directrix is $x + y - 2 = 0$,find the vertex.

Let $LL^{\prime}$ be the latus rectum and $PQ$ be the focal chord of the parabola $y^2=16x$. If $P=(1,4)$ and $P, L$ lie in the same quadrant,then $LQ=$

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

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.

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

Let $P$ be the parabola in the plane determined by the equation $y = x^2$. Suppose a circle $C$ in the plane intersects $P$ at four distinct points. If three of these points are $(17, 289), (-2, 4), (13, 169)$,then the sum of the perpendicular distances from the directrix of $P$ to all four of the intersection points is:

If the focal chord drawn through the point $P(5,5)$ to the parabola $y^2=5x$ meets the parabola again at the point $Q$,then the tangent drawn to this parabola at $Q$ meets the axis of the parabola at the point