If the parabola $y^2 = 4ax$ passes through the point $(-3, 2)$,then the length of its latus rectum is

Find the area of the triangle formed by the lines joining the vertex of the parabola $x^{2}=12y$ to the ends of its latus rectum. (in $\text{ unit}^{2}$)

Find the equation of the normal to the parabola $y^2 = 4x$ passing through the point $(3, 0)$.

The equation of a tangent line to the parabola $y^2 = 8x$,which passes through the point $(1, 3)$,is:

Find the directrix of the locus of the midpoint of the line segment joining the focus and a variable point on the parabola $y^{2} = 4ax$.

The length of the chord of the parabola $y^2 = 4ax$ which passes through the vertex and makes an angle $\theta$ with the axis of the parabola is: