What are the parametric equations of the parabola $(y - 2)^2 = 12(x - 4)$?

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 $(a, 0)$

If a parabola having its axis parallel to the $X$-axis passes through the points $(0, -1)$,$(6, 1)$,and $(-2, -3)$,then the point at which this parabola cuts the $X$-axis is

The latus rectum of a parabola whose focal chord $PSQ$ is such that $SP = 3$ and $SQ = 2$ is given by

If $S(a, b)$ is a fixed point and $P(\alpha, \beta)$ is a variable point such that $4[(x-a)^2+(y-b)^2]=(\alpha x+\beta y+7)^2$ represents a parabola,then the locus of $P(\alpha, \beta)$ is

If the normal to the parabola $y^2 = 4ax$ at the point with parameter $t_1$ cuts the parabola again at the point with parameter $t_2$,then: