If the parabola $x^{2} = 4ay$ passes through the point $(2, 1)$,then the length of the latus rectum is

$AB$ is a chord of a parabola $y^2 = 4ax, (a > 0)$ with vertex $A$. $BC$ is drawn perpendicular to $AB$ meeting the axis at $C$. The projection of $BC$ on the axis of the parabola is

$PQ$ is a double ordinate of the parabola $y^2 = 4ax$. The locus of the points of trisection of $PQ$ is

The equation of the parabola whose vertex and focus lie on the $x$-axis at distances $a$ and $a'$ from the origin,respectively,is

What is the value of the parameter $t$ for the point $(2, 6)$ on the parabola $y^2 = 18x$?

If $(h, k)$ is the point to which the origin is shifted in order to transform the equation $y^2-4x+6y+17=0$ into the form $Y^2=4aX$,then $h^2+k^2=$