Let $y^2 = 12x$ be the parabola with its vertex at $O$. Let $P$ be a point on the parabola and $A$ be a point on the $x$-axis such that $\angle OPA = 90^\circ$. Then the locus of the centroid of such triangles $OPA$ is:

If the system of equations

$ 3x + y + 4z = 3 $

$ 2x + \alpha y - z = -3 $

$ x + 2y + z = 4 $

has no solution, then the value of $ \alpha $ is equal to:

Let $z$ be the complex number satisfying $|z-5| \leq 3$ and having maximum positive principal argument.

Then $34 \left| \frac{5z - 12}{5iz + 16} \right|^2$ is equal to: