The equations $x = \frac{t}{4}$ and $y = \frac{t^2}{4}$ represent:

Let a parabola $P$ be such that its vertex and focus lie on the positive $x$-axis at a distance $2$ and $4$ units from the origin,respectively. If tangents are drawn from $O(0,0)$ to the parabola $P$ which meet $P$ at $S$ and $R$,then the area (in $sq. \text{ units}$) of $\triangle SOR$ is equal to:

The equation of the parabola with $x+2y=1$ as directrix and $(1,0)$ as focus is

How many parabolas can be drawn if the two endpoints of the latus rectum are given?

What is the vertex of the parabola $x^2 - 8y - x + 19 = 0$?

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