For a parabola with focus $(2, 1)$ and directrix $2x - 3y + 1 = 0$,what is the equation of the latus rectum?

The vertex of the parabola $(y - 2)^2 = 16(x - 1)$ is

What is the length of the latus rectum of the parabola $x = ay^2 + by + c$?

$A$ 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 $1 \, cm$?

The length of the subnormal to any point of a curve is constant. Then,the eccentricity of the curve is . . . . . .

Let $x+y=k$ be a normal to the parabola $y^2=12x$. If $p$ is the length of the perpendicular from the focus of the parabola onto this normal,then $4k-2p^2$ is equal to