If the perpendicular distance from the focus of a parabola $y^2=4ax$ to its directrix is $\frac{3}{2}$,then the equation of the normal drawn at $(4a, -4a)$ is

Find the length of the chord of the parabola $y^2 = 4x$ which passes through the vertex and makes an angle of $30^{\circ}$ with the $x$-axis. (in $\sqrt{3}$)

The area of the triangle formed by the lines joining the vertex of the parabola $x^{2}=12y$ to the ends of the latus rectum is

$S \equiv y^2 - 4ax = 0$ and $S' \equiv y^2 + ax = 0$ are two parabolas,and $P(t)$ is a point on the parabola $S' = 0$. If $A$ and $B$ are the feet of the perpendiculars from $P$ onto the coordinate axes and $AB$ is a tangent to the parabola $S = 0$ at the point $Q(t_1)$,then $t_1 =$

The points of intersection of the parabolas $y^2=5x$ and $x^2=5y$ lie on the line

The length of the normal chord of the parabola $y^2 = 4x$,which makes an angle of $\frac{\pi}{4}$ with the $x$-axis,is: