If the three normals drawn to the parabola $y^{2} = 2x$ pass through the point $(a, 0)$ where $a \neq 0$,then $a$ must be greater than:

The equation of the common tangent of the parabolas $x^2=108y$ and $y^2=32x$ is

If a normal drawn to the parabola $y^2 = 4ax$ at the point $(a, 2a)$ meets the parabola again at $(at^2, 2at)$,then the value of $t$ is:

If the normal at the point $t_1$ (i.e.,at $(at_1^2, 2at_1)$) on the parabola $y^2 = 4ax$ meets the parabola again at the point $t_2$,then $t_1t_2$ is equal to:

The line $x + y = 6$ is a normal to the parabola $y^2 = 8x$ at the point

Let the tangent to the parabola $S: y^{2}=2x$ at the point $P(2,2)$ meet the $x$-axis at $Q$ and the normal at $P$ meet the parabola $S$ at the point $R$. Then the area (in $sq. \ units$) of the triangle $PQR$ is equal to: