What is the focus of the parabola $4y^2 + 12x - 20y + 67 = 0$?

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.

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

The equation of the parabola whose vertex is $(-1, -2)$,axis is vertical and which passes through the point $(3, 6)$,is

An equilateral triangle is inscribed in the parabola $y^{2}=4ax$,where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

If $y=4x+3$ is parallel to a tangent to the parabola $y^{2}=12x$,then its distance from the normal parallel to the given line is

The locus of the middle points of the chords of the parabola $y^2 = 4ax$ which pass through the origin is: