The line $y = 2x + c$ is tangent to the parabola $y^2 = 4x$,then $c = $

If $(x_1, y_1)$ and $(x_2, y_2)$ are the endpoints of a focal chord of the parabola $y^2 = 4ax$,then what is the square of the $G.M.$ of $x_1$ and $x_2$?

Let $P$ represent the point $(3, 6)$ on the parabola $y^2 = 12x$. For the parabola $y^2 = 12x$,if $l_1$ is the length of the normal chord drawn at $P$ and $l_2$ is the length of the focal chord drawn through $P$,then $\frac{l_1}{l_2} = $

If the normal drawn at the point $P(9, 9)$ on the parabola $y^2 = 9x$ meets the parabola again at $Q(a, b)$,then $2a + b =$

The point at which the line $y = mx + c$ touches the parabola $y^2 = 4ax$ 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