Find the equation of the parabola that satisfies the following conditions: Focus $(0, -3)$,directrix $y = 3$.

Suppose $AB$ is a focal chord of the parabola $y^2=12x$ of length $l$ and slope $m < \sqrt{3}$. If the distance of the chord $AB$ from the origin is $d$,then $l \cdot d^2$ is equal to ....................

$A$ point $P$ moves such that the sum of the angles which the three normals drawn from $P$ to the standard parabola $y^2 = 4ax$ make with the axis of the parabola is constant. Then the locus of $P$ is:

The parametric equations of the parabola $y^2 - 12x - 2y - 11 = 0$ are:

The vertex of the parabola $3x - 2y^2 - 4y + 7 = 0$ is

$A$ circle is drawn with its centre at the focus of the parabola $y^2 = 2px$ such that it touches the directrix of the parabola. Then a point of intersection of the circle and the parabola is