The equation of the latus rectum of the parabola $x^2 + 4x + 2y = 0$ is:

If the line $x-y=-4K$ is a tangent to the parabola $y^2=8x$ at $P$,then the perpendicular distance of the normal at $P$ from $(K, 2K)$ is

The normal at a point on the parabola $y^2=4x$ passes through $(5,0)$. If there are two more normals to this parabola which pass through $(5,0)$,the centroid of the triangle formed by the feet of these three normals is

If $x = t^2$ and $y = 2t$,then the equation of the normal at $t = 1$ is

From a point $(d, 0)$, three normals are drawn to the parabola $y^{2} = x$. Then:

The line $x \cos \alpha + y \sin \alpha = p$ will touch the parabola $y^2 = 4a(x + a)$ if: