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

An arch is in the form of a parabola with its axis vertical. The arch is $10 \, m$ high and $5 \, m$ wide at the base. How wide is it $2 \, m$ from the vertex of the parabola (in $, m$)?

If one end of a focal chord of the parabola $y^2 = 16x$ is at $(1, 4)$,then the length of this focal chord is

Let $C$ be the locus of the mirror image of a point on the parabola $y^{2}=4x$ with respect to the line $y=x$. Then the equation of the tangent to $C$ at $P(2,1)$ is:

If the normal chord drawn at the point $\left(\frac{15}{2}, \frac{15}{\sqrt{2}}\right)$ to the parabola $y^2=15x$ subtends an angle $\theta$ at the vertex of the parabola,then $\sin \frac{\theta}{3}+\cos \frac{2\theta}{3}-\sec \frac{4\theta}{3}=$

If $(-1,-1)$ is the focus and $x+y+4=0$ is the directrix of a parabola,then its vertex is