If $y = 2x - 3$ is a tangent to the parabola $y^2 = 4a(x - \frac{1}{3})$,then $a$ is equal to:

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

The locus of the poles of focal chords of the parabola $y^2 = 4ax$ is

If $A(at^2, 2at)$,$B(a/t^2, -2a/t)$,and $C(a, 0)$,then $2a$ is equal to

Normals at $P, Q, R$ are drawn to the parabola $y^2 = 4x$ which intersect at the point $(3, 0)$. Then,$\Delta PQR$ is:

If the line $2x + 3y + n = 0$ is a tangent to the parabola $y^2 = 8x$,then the equation of the normal drawn at the point $(2n, 4\sqrt{n})$ to the parabola $y^2 = 8x$ is