Find the equation of the parabola with vertex at $(0, 0)$ and focus at $(0, 2)$.

The length of the latus rectum of the parabola whose focus is $(3,3)$ and directrix is $3x - 4y - 2 = 0$ is . . . . . . units.

The equation of the directrix of the parabola ${x^2} + 8y - 2x = 7$ is

Two parabolas have the same focus $(4, 3)$ and their directrices are the $x$-axis and the $y$-axis,respectively. If these parabolas intersect at the points $A$ and $B$,then $(AB)^2$ is equal to

The equation of the directrix of the parabola $x^2+8x+12y+4=0$ is

In the $XY$-plane,three distinct lines $l_1, l_2, l_3$ concur at a point $(\lambda, 0)$. Further,the lines $l_1, l_2, l_3$ are normals to the parabola $y^2=6x$ at the points $A=(x_1, y_1)$,$B=(x_2, y_2)$,and $C=(x_3, y_3)$ respectively. Then,we have: