The slope of the normal at the point $(at^2, 2at)$ of the parabola $y^2 = 4ax$ is

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:

Find the equation of the tangent at the vertex of the parabola $4y^2 + 6x = 8y + 7$.

The length of the subnormal to the parabola $y^2 = 4ax$ at any point is equal to

If $x = my + c$ is a normal to the parabola ${x^2} = 4ay$,then the value of $c$ is

The equation of the common tangent of the parabolas $x^2=108y$ and $y^2=32x$ is