If a normal drawn to the parabola $y^2 = 4ax$ at the point $(a, 2a)$ meets the parabola again at $(at^2, 2at)$,then the value of $t$ is:

Three normals are drawn from the point $(c, 0)$ to the curve $y^2=x$. If one of the normals is the $X$-axis,then the value of $c$ for which the other two normals are perpendicular to each other is

If $(2,0)$ is the vertex and the $Y$-axis is the directrix of a parabola,then its focus is

The pole of the line $lx + my + n = 0$ with respect to the parabola $y^{2} = 4ax$ is

Let the line $y - \sqrt{3}x + 3 = 0$ cut the parabola $2y^2 = 2x + 3$ at $A$ and $B$. If $P(\sqrt{3}, 0)$,then the value of $|PA - PB|$ is [where $PA$ denotes the distance between points $P$ and $A$].

The locus of the point of intersection of the normals to the parabola $x^2=8y$,which are at right angles to each other,is