The straight line $y = 2x + \lambda$ does not meet the parabola $y^2 = 2x$,if

If $x = my + c$ is a normal to the parabola ${x^2} = 4ay$,then the value of $c$ is

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

Let $x=2t, y=\frac{t^2}{3}$ be a conic. Let $S$ be the focus and $B$ be the point $(0, \alpha)$ on the axis of the conic such that $SA \perp BA$,where $A$ is any point $(2t, \frac{t^2}{3})$ on the conic. If $k$ is the ordinate of the centroid of $\Delta SAB$,then $\lim_{t \rightarrow 1} k$ is equal to

If the focus of a parabola divides a focal chord of the parabola into segments of lengths $5$ and $3$ units,then the length of the latus rectum of that parabola is:

The locus of the mid-points of all chords of the parabola $y^{2}=4ax$ passing through its vertex is another parabola with directrix: