Let $L L^{\prime}$ be the latusrectum and $P Q$ be the focal chord of the parabola $y^2=16 x$. If $P=(1,4)$ and $P, L$ lie in the same quadrant, then $L Q=$

If $P\left(\frac{1}{2}, 4\right)$ and $Q$ are the ends of a focal chord of the parabola $y^2=32 x$ and $S$ is the focus of the parabola, then $S Q=$

If the distance from a variable point $P$ to a fixed point $A(a, 0)$ is equal to the perpendicular distance from $P$ to the line $x+y=0$, then the equation of the locus of $P$ is

The point to which the origin is to be shifted by translation of axes so that the transformed equation of $y^2+4 y+8 x-2=0$ will not contain $y$ term and constant term is