Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$,focus $(-2, 0)$.

Two parabolas with a common vertex at the origin and with axes along the $x-$ axis and $y-$ axis,respectively,intersect each other in the first quadrant. If the length of the latus rectum of each parabola is $3$,then the equation of the common tangent to the two parabolas is?

Let the length of the focal chord $PQ$ of the parabola $y^2=12x$ be $15$ units. If the distance of $PQ$ from the origin is $p$,then $10p^2$ is equal to:

If the axis of a parabola is horizontal and it passes through the points $(0, 0), (0, -1)$ and $(6, 1)$,then its equation is

The parabola with focus at $(4, -3)$ and vertex at $(4, -1)$ is

The equation of any normal to the parabola ${y^2} = 4a(x - a)$ is