If the focus of a parabola is $(0,-3)$ and its directrix is $y=3$,then its equation is

If tangent lines are drawn from the point $(-1, 2)$ to the parabola $y^2 = 4x$, then the area of the triangle (in sq. units) formed by the chord of contact and the tangents drawn is: (in $\sqrt{2}$)

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

Let $PQ$ be a double ordinate of the parabola $y^2 = -4x$,where $P$ lies in the second quadrant. If $R$ divides $PQ$ in the ratio $2 : 1$,then the locus of $R$ is:

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola $y^2=4ax$ is a conic. The equation of the directrix of that conic is

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