How many parabolas can be drawn if the two endpoints of the latus rectum are given?

Three normals are drawn from the point $(3, 0)$ to the parabola $y^2 = 4x$,meeting the parabola at points $P, Q,$ and $R$. Match the following:

Column-$I$	Column-$II$
$(A)$ Circumradius of $\Delta PQR$	$(P)$ $5/2$
$(B)$ Area of $\Delta PQR$	$(Q)$ $(5/2, 0)$
$(C)$ Centroid of $\Delta PQR$	$(R)$ $(2/3, 0)$
$(D)$ Circumcenter of $\Delta PQR$	$(S)$ $2$

Let the equation of the tangent at a point $P$ on the parabola $x^2-4x-4y+16=0$ be $2x-y-5=0$. If the equation of the normal drawn at $P$ to this parabola is $ax+y+c=0$,then find the value of $ac$.

The tangents to the parabola $y^2 = 4ax$ make angles $\theta_1$ and $\theta_2$ with the positive $x$-axis. If $\cot \theta_1 + \cot \theta_2 = c$,then the locus of their point of intersection is

The equation of the normal to the parabola $y^{2} = x + a$ with slope $m$ is .....

The points of contact $Q$ and $R$ of the tangents drawn from the point $P(2, 3)$ to the parabola $y^2 = 4x$ are