An arch is in the form of a parabola with its axis vertical. The arch is $10 \, m$ high and $5 \, m$ wide at the base. How wide is it $2 \, m$ from the vertex of the parabola (in $, m$)?

The end points of the latus rectum of the parabola $x^2 = 4ay$ are

Let $P$ be a point on the parabola $y^{2}=12x$ and $N$ be the foot of the perpendicular drawn from $P$ on the axis of the parabola. $A$ line is drawn through the mid-point $M$ of $PN$,parallel to the axis of the parabola,which meets the parabola at $Q$. If the $y$-intercept of the line $NQ$ is $\frac{4}{9}$,then:

If $P(-3, 2)$ is an end point of the focal chord $PQ$ of the parabola $y^2 + 4x + 4y = 0$,then the slope of the normal drawn at $Q$ is

Let $LL^{\prime}$ be the latus rectum and $PQ$ be the focal chord of the parabola $y^2=16x$. If $P=(1,4)$ and $P, L$ lie in the same quadrant,then $LQ=$

If the normals at points $t_1$ and $t_2$ on the parabola $y^2 = 4ax$ intersect again on the parabola,then what is the value of $t_1t_2$?