Find the equation of the directrix of the parabola $y^2 = 12x$.

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4x$ is

The condition for which the straight line $y = mx + c$ touches the parabola $y^2 = 4ax$ is

The perpendicular distance from the origin to the focal chord drawn through the point $(4, 5)$ to the parabola $y^2 - 4y - 3x + 7 = 0$ 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 passing through $(5,0)$,then the equation of one of these normals is

If $y=4x+3$ is parallel to a tangent to the parabola $y^{2}=12x$, then its distance from the normal parallel to the given line is