If one of the vertices of an equilateral triangle inscribed in the parabola $y^2=12x$ coincides with the vertex of the parabola, then the area (in sq. units) of that triangle is (in $\sqrt{3}$)

If $5x - 2y + k = 0$ is a tangent to the parabola $y^2 = 6x$,then their point of contact is

The straight line $y = 2x + \lambda$ does not meet the parabola $y^2 = 2x$,if

The line $x-2y-3=0$ cuts the parabola $y^2=4ax$ at the points $P$ and $Q$. If the focus of this parabola is $(\frac{1}{4}, k)$,then $PQ=$

The normal at a point on the parabola $y^2 = 4x$ passes through a point $P$. Two more normals to this parabola also pass through $P$. If the centroid of the triangle formed by the feet of these three normals is $G(2,0)$,then the abscissa of $P$ is

If $x = t^{2} + 2$ and $y = 2t$ represent the parametric equations of a parabola,find its Cartesian equation.