The locus of the mid-point of the line segment joining the focus and any point on the parabola $y^{2}=4ax$ is a parabola. Find the equation of its directrix.

The equation of the tangent to the parabola $y^2 = 9x$ which passes through the point $(4, 10)$ is:

The normal at a point on the parabola $y^2=4x$ passes through $(5,0)$. If there are two more normals to this parabola which pass through $(5,0)$,the centroid of the triangle formed by the feet of these three normals is

Let a parabola $P$ be such that its vertex and focus lie on the positive $x$-axis at a distance $2$ and $4$ units from the origin,respectively. If tangents are drawn from $O(0,0)$ to the parabola $P$ which meet $P$ at $S$ and $R$,then the area (in $sq. \text{ units}$) of $\triangle SOR$ is equal to:

Tangents are drawn from the point $(-1, 2)$ to the parabola $y^2 = 4x$. The length of the intercept made by these tangents on the line $x = 2$ is:

Let the normal at the point $P$ on the parabola $y^{2} = 6x$ pass through the point $(5, -8)$. If the tangent at $P$ to the parabola intersects its directrix at the point $Q$,then the ordinate of the point $Q$ is