Find the length of the latus rectum of a parabola if $PSQ$ is a focal chord such that $SP = 3$ and $SQ = 2$.

The equation of the parabola whose focus is $(5, 3)$ and directrix is $3x - 4y + 1 = 0$ is:

If $(2,3)$ is the focus and $x-y+3=0$ is the directrix of a parabola,then the equation of the tangent drawn at the vertex of the parabola is

If the normal at the point $t_1$ (i.e.,at $(at_1^2, 2at_1)$) on the parabola $y^2 = 4ax$ meets the parabola again at the point $t_2$,then $t_1t_2$ is equal to:

The area of the triangle formed by the lines joining the vertex of the parabola,$x^2 = 8y$,to the extremities of its latus rectum is

If $P(-3, 2)$ is an end point of the focal chord $PQ$ of the parabola $y^2 + 4x + 4y = 0$,then the slope of the normal drawn at $Q$ is