If $(2,0)$ is the vertex and the $Y$-axis is the directrix of a parabola,then its focus is

Let $P(4, -4)$ and $Q(9, 6)$ be two points on the parabola $y^2 = 4x$. Let $X$ be any point on the arc $POQ$ of this parabola,where $O$ is the vertex,such that the area of $\Delta PXQ$ is maximum. Then this maximum area (in sq. units) is

The equation of the tangent to the parabola $y^2 = 4ax$ at the point $(a/t^2, 2a/t)$ is:

Let $O$ be the origin and $A$ be a point on the curve $y^2=4x$. Then the locus of the midpoint of $OA$ is:

An equilateral triangle is inscribed in the parabola $y^2=16ax$ with one of its vertices at the origin. Then,the centroid of that triangle is

If the vertex and focus of a parabola lying on the $x$-axis are at distances $p$ and $q$ from the origin respectively,find its equation.