The area of the triangle formed by the lines joining the vertex of the parabola $x^{2}=12y$ to the ends of the latus rectum is

The length of the latus rectum of a parabola,whose vertex and focus are on the positive $x$-axis at a distance $R$ and $S$ $(S > R)$ respectively from the origin,is:

The equation of the common tangent drawn to the curves $y^2 = 8x$ and $xy = -1$ is

Consider the parabola with vertex $\left(\frac{1}{2}, \frac{3}{4}\right)$ and the directrix $y=\frac{1}{2}$. Let $P$ be the point where the parabola meets the line $x=-\frac{1}{2}$. If the normal to the parabola at $P$ intersects the parabola again at the point $Q$,then $(PQ)^{2}$ is equal to :

If a perpendicular drawn through the vertex $O$ of the parabola $y^2=4ax$ to any of its tangent meets the tangent at $N$ and the parabola at $M$,then $ON \cdot OM=$

If the line $2x - 3y = k$ is tangent to the parabola $y^2 = 6x$,then what is the value of $k$?