The length of the latus rectum of the parabola $y^2 - 4y - 2x - 8 = 0$ is:

The normal at a point on the parabola $y^2 = 4x$ passes through a point $P$. Two more normals to this parabola also pass through $P$. If the centroid of the triangle formed by the feet of these three normals is $G(2,0)$,then the abscissa of $P$ is

$PQ$ is any focal chord of the parabola $y^2=32x$. The length of $PQ$ can never be less than: ............ $unit$

Let a line $y=mx$ $(m>0)$ intersect the parabola $y^{2}=x$ at a point $P$,other than the origin. Let the tangent to it at $P$ meet the $x$-axis at the point $Q$. If $\text{area}(\Delta OPQ)=4$ sq. units,then $m$ is equal to

Find the coordinates of the focus,axis of the parabola,the equation of the directrix,and the length of the latus rectum for $x^{2}=-9y$.

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is