If the focus of the parabola is $(3, -4)$ and the directrix is $y - 4 = 0,$ then the equation of the parabola is :-

Let $x+y=k$ be a normal to the parabola $y^2=12x$. If $p$ is the length of the perpendicular from the focus of the parabola onto this normal,then $4k-2p^2$ is equal to

On the parabola $y = x^2$,the point at the least distance from the straight line $y = 2x - 4$ is

If the angle between the tangents drawn through the point $(-2, -1)$ to the parabola $y^2 = 4x$ is $\theta$,then $\tan 2\theta =$

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:

The length of the latus rectum of the parabola $9x^2 + 16y^2 + 24xy - 4x + 3y = 0$ is