Parabola

Equation of the common tangent touching the circle $(x-3)^2+y^2=9$ and the parabola $y^2=4x$ above the $x$-axis is

Vertex of parabola $ y^{2} - 8y + 19 = 0 $

If $x = 1$ is the directrix of the parabola $y^{2} = kx - 8$, then k is:

An equilateral triangle is inscribed in the parabola $y^{2} = 4ax$, such that one of the vertices of the triangle coincides with the vertex of the parabola. The length of the side of the triangle is:

The locus of the mid points of all chords of the parabola $y^{2}=4x$ which are drawn through its vertex, is