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

An equilateral triangle is inscribed in the parabola $y^2 = 4ax$ such that one of its vertices is at the origin $(0, 0)$ and the other two vertices lie on the parabola. The length of its side is equal to

The normal to the parabola ${y^2 = 8x}$ at the point $(2, 4)$ meets the parabola again at the point

Let $A$ and $B$ be the two points of intersection of the line $y+5=0$ and the mirror image of the parabola $y^2=4x$ with respect to the line $x+y+4=0$. If $d$ denotes the distance between $A$ and $B$,and $a$ denotes the area of $\triangle SAB$,where $S$ is the focus of the parabola $y^2=4x$,then the value of $(a+d)$ is:

Find the equation of the normal to the curve $x^{2}=4y$ which passes through the point $(1, 2)$.

What is the equation of the tangent to the parabola $y^2 = 4x$ at the point $(1, 2)$?