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

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 ....................

Three normals are drawn from the point $(c, 0)$ to the curve $y^2=x$. If one of the normals is the $X$-axis,then the value of $c$ for which the other two normals are perpendicular to each other is

The maximum number of points on the parabola $y^2 = 16x$ that are equidistant from a variable point $P$ (which lies inside the parabola) is -

The line $y=x+1$ is a tangent to the curve $y^{2}=4x$ at the point

Find the equation of the parabola with focus $(2, 0)$ and directrix $x = -2$.