If one of the vertices of an equilateral triangle inscribed in the parabola $y^2=12 x$ coincides with the vertex of the parabola, then the area (in sq units) of that triangle is

If $x-2 y+k=0$ is a tangent to the parabola $y^2-4 x-4 y+8=0$, then the value of $k$ is

If the points of intersection of the parabolas $y^2=5 x$ and $x^2=5 y$ lie on the line $L$, then the area of the triangle formed by the directrix of one parabola, latus rectum of another parabola and the line $L$ is

If the line $2 x+3 y+n=0$ is a tangent to the parabola $y^2=8 x$, then the equation of the normal drawn at the point $(2 n, 4 \sqrt{n})$ to the parabola $y^2=8 x$ is