What is the slope of the normal to the parabola $x^2 + 4y = 0$ at the point $(2, -1)$?

If the segment of the parabola $y^2 = 4ax$ intercepted by its directrix subtends an angle $\theta$ at its focus,then $\theta = \dots$

If the vertex of a parabola is $(2, -1)$ and the equation of its directrix is $4x - 3y = 21$,then the length of its latus rectum is

The latus rectum of a parabola whose focal chord $PSQ$ is such that $SP = 3$ and $SQ = 2$ is given by

Let the focal chord $PQ$ of the parabola $y^2=4x$ make an angle of $60^{\circ}$ with the positive $x$-axis,where $P$ lies in the first quadrant. If the circle,whose one diameter is $PS$,$S$ being the focus of the parabola,touches the $y$-axis at the point $(0, \alpha)$,then $5 \alpha^2$ is equal to :

The equation of the parabola whose vertex and focus lie on the $x$-axis at distances $a$ and $a'$ from the origin,respectively,is