The length of the latus rectum of the parabola $y^2 - 4y - 2x - 8 = 0$ is:

Find the minimum distance from the point $(0, c)$ to the parabola $y = x^2$,where $0 \leq c \leq 5$.

$A$ tangent is drawn to the parabola $y^{2}=6x$ which is perpendicular to the line $2x+y=1$. Which of the following points does $NOT$ lie on it?

If $lx + my + n = 0$ is tangent to the parabola $x^2 = y$,then the condition of tangency is

If the line $x-y=-4K$ is a tangent to the parabola $y^2=8x$ at $P$,then the perpendicular distance of the normal at $P$ from $(K, 2K)$ is

The area of the triangle formed by the lines joining the vertex of the parabola,$x^2 = 8y$,to the extremities of its latus rectum is