If the straight line $y=mx+c$ is parallel to the axis of the parabola $y^2=lx$ and intersects the parabola at $\left(\frac{c^2}{8}, c\right)$,then the length of the latus rectum is

The length of the latus rectum of the parabola $y^2+8x-2y+17=0$ is

If $x^2 = 8ay$ is the transformed equation of $x^2 - 4y + 6x + 15 = 0$ when the origin is shifted to the point $(\alpha, \beta)$ by translation of axes,then $2\alpha + 8\beta^2 =$

The length of the latus rectum of the parabola whose focus is at $(1, -2)$ and directrix is the line $x + y + 3 = 0$ is

The normal to the parabola ${y^2 = 8x}$ at the point $(2, 4)$ meets the parabola again at the point

If the normal at one end of the latus rectum of the parabola $y^2=16x$ meets the $X$-axis at the point $P$, then the length of the chord passing through $P$ and perpendicular to the normal is (in $\sqrt{2}$)