Find the equation of the directrix of the parabola $y^2 = 12x$.

Three normals to the parabola $y^2 = x$ are drawn through a point $(C, 0)$. Then:

An equilateral triangle is inscribed in the parabola $y^2 = 4ax$ such that one of its vertices is at the origin $(0, 0)$ and the other two vertices lie on the parabola. The length of its side is equal to

If the angle between the tangents drawn to the parabola $y^2 = 4x$ from a point on the line $4x - y = 0$ is $\frac{\pi}{3}$,then the sum of the abscissae of all such points is

The vertex of the parabola $9x^2 - 6x + 36y + 9 = 0$ is

Let $P$ be the mid-point of a chord joining the vertex of the parabola $y^{2}=8x$ to another point on it. Then,the locus of $P$ is