The equation of the tangent to the parabola $y^2=8x$,which is parallel to the line $4x-y+3=0$,is

If the line $y = mx + c$ is a tangent to the parabola $y^2 = 4a(x + a)$,then $ma + \frac{a}{m}$ is equal to

The straight line joining any point $P$ on the parabola $y^2 = 4ax$ to the vertex and the perpendicular from the focus to the tangent at $P$ intersect at $R$. Then the equation of the locus of $R$ is:

Let $x+y=k$ be a normal to the parabola $y^2=12x$. If $p$ is the length of the perpendicular from the focus of the parabola onto this normal,then $4k-2p^2$ is equal to

The equation of the directrix of the parabola $y^2+4y+4x+2=0$ is

The locus of the point of intersection of the perpendicular tangents to the parabola $x^2 = 4ay$ is