The line $x - 1 = 0$ is the directrix of the parabola ${y^2} - kx + 8 = 0$. Then one of the values of $k$ is

$A$ beam is supported at its ends by supports which are $12 \, m$ apart. Since the load is concentrated at its centre,there is a deflection of $3 \, cm$ at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection $1 \, cm$?

In the $XY$-plane,three distinct lines $l_1, l_2, l_3$ concur at a point $(\lambda, 0)$. Further,the lines $l_1, l_2, l_3$ are normals to the parabola $y^2=6x$ at the points $A=(x_1, y_1)$,$B=(x_2, y_2)$,and $C=(x_3, y_3)$ respectively. Then,we have:

For the parabola represented in the parametric form by $x=t^2+t+1$ and $y=t^2-t+1$,the length of the latus rectum is

If three points $P, Q, R$ on the parabola $y^2 = 4ax$ are such that their ordinates are in geometric progression,then the tangents at $P$ and $R$ intersect on:

Find the point of contact of the line $2x - y + 2 = 0$ with the parabola $y^2 = 16x$.