If a normal is drawn to the parabola $y^2 = 4ax$ at the point $(2a, 2\sqrt{2}a)$,what is the length of the normal chord?

$A$ circle of radius $2$ unit passes through the vertex and the focus of the parabola $y^{2}=2x$ and touches the parabola $y=\left(x-\frac{1}{4}\right)^{2}+\alpha$,where $\alpha>0$. Then $(4\alpha-8)^{2}$ is equal to

If the focus divides a focal chord of the parabola $y^2 = 16x$ into $2$ parts having lengths $a$ and $c$,such that $a, b, c$ are in $H.P.$,then the value of $b$ is equal to:

The angle of intersection between the curves $y^2 = 4x$ and $x^2 = 32y$ at the point $(16, 8)$ is:

The angle between the two curves $y^2 = 4(x + 1)$ and $x^2 = 4(y + 1)$ is .............. $^\circ$.

From the focus of the parabola $y^2 = 12x$, a ray of light is directed in a direction making an angle $\tan^{-1} \frac{3}{4}$ with the $x$-axis. Then the equation of the line along which the reflected ray leaves the parabola is