The distance of the point $(6, 4 \sqrt{3})$ from the focus of the parabola $y^2 = 8x$ is:

The locus of a point which divides the line segment joining the point $(0,-1)$ and a point on the parabola $x^{2}=4y$ internally in the ratio $1:2$ is:

If $P_1 P_2$ and $P_3 P_4$ are two focal chords of the parabola $y^2 = 4ax$, then the chords $P_1 P_3$ and $P_2 P_4$ intersect on the

The length intercepted by the curve $y^2 = 4x$ on the line satisfying $dy/dx = 1$ and passing through the point $(0, 1)$ is given by

If the normal at point $P(t)$ to the parabola $y^2 = 16x$ meets it again at point $Q(36, -24)$,then the maximum possible focal distance of point $P$ is-

Let the tangent and normal at any point $P(at^2, 2at)$, $(a > 0)$, on the parabola $y^2 = 4ax$ meet the axis of the parabola at $T$ and $G$ respectively. Then the radius of the circle through $P, T$ and $G$ is