The coordinates of a point on the parabola $y^2 = 8x$ whose focal distance is $4$ are

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4x$ is

Let $M$ be the foot of the perpendicular from a point $P$ on the parabola $y^2=8(x-3)$ onto its directrix and let $S$ be the focus of the parabola. If $\triangle SPM$ is an equilateral triangle,then $P$ is equal to

The tangent $PT$ and the normal $PN$ to the parabola $y^2=4ax$ at a point $P$ on it meet its axis at points $T$ and $N$,respectively. The locus of the centroid of the triangle $PTN$ is a parabola whose
$(A)$ vertex is $\left(\frac{2a}{3}, 0\right)$
$(B)$ directrix is $x=0$
$(C)$ latus rectum is $\frac{2a}{3}$
$(D)$ focus is $(a, 0)$

The vertex of the parabola $x^2 + 4x + 2y - 7 = 0$ is

$PQ$ is a double ordinate of the parabola $y^2 = 4ax$. The locus of the points of trisection of $PQ$ is