Find the equation of the latus rectum of the parabola $x^2 = -12y$.

$TP$ and $TQ$ are tangents of the parabola $y^2 = 8x$ at $P$ and $Q$ respectively. If the chord $PQ$ passes through the point $(-2, 3)$ and the locus of point $T$ is $y = mx + c$,then $(m + c)$ is equal to -

If a focal chord of the parabola $y^2 = 4x$ makes an angle $45^{\circ}$ with the positive $X$-axis,then the slopes of the normals drawn at the ends of the focal chord will satisfy the equation:

$A$ 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 $1 \, cm$?

$A$ point on the parabola $y^2 = 18x$ at which the ordinate increases at twice the rate of the abscissa is

If the focus divides a focal chord of the parabola $y^2 = 16x$ into $2$ parts having lengths $a$ and $c$,such that $a, b, c$ are in $H.P.$,then the value of $b$ is equal to: