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

If the normals drawn at the points $P\left(\frac{3}{4}, \frac{3}{2}\right)$ and $Q(3,3)$ on the parabola $y^2=3x$ intersect again on the parabola at $R$,then $R=$

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

If the chord joining the points $P_{1}(x_{1}, y_{1})$ and $P_{2}(x_{2}, y_{2})$ on the parabola $y^{2} = 12x$ subtends a right angle at the vertex of the parabola, then $x_{1}x_{2} - y_{1}y_{2}$ is equal to

If one end of a focal chord of the parabola $y^2 = 16x$ is at $(1, 4)$,then the length of this focal chord is

The sum of squares of all possible values of $k$,for which the area of the region bounded by the parabolas $2y^2 = kx$ and $ky^2 = 2(y - x)$ is maximum,is equal to: