The parabola $y^2 = x$ is symmetric about

The shortest distance between the line $y = x$ and the curve $y^2 = x - 2$ is

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is

The locus of the feet of the perpendiculars drawn from the vertex of the parabola $y^2 = 4ax$ upon all such chords of the parabola which subtend a right angle at the vertex is

The directrix of the parabola $2 y^2+25 x=0$ is $........$

Find the length of the latus rectum of the parabola whose focus is $(2, 3)$ and the directrix is the line $x - 4y + 3 = 0$.