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

Let $A$ be the focus of the parabola $y^{2}=8x$. Let the line $y=mx+c$ intersect the parabola at two distinct points $B$ and $C$. If the centroid of the triangle $ABC$ is $(\frac{7}{3},\frac{4}{3})$, then $(BC)^{2}$ is equal to:

Find the parametric coordinates of any point on the parabola whose focus is $(0, 1)$ and directrix is $x + 2 = 0$.

The slope of the line touching both the parabolas $y^2 = 4x$ and $x^2 = -32y$ is

If the lines $2x + 3y + 12 = 0$ and $x - y + k = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $k$ is equal to

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