For the parabola $y^2 = 4ax$,what is the $x$-coordinate of the point closest to the focus?

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

The equation of the parabola whose focus is the point $(0, 0)$ and the tangent at the vertex is $x - y + 1 = 0$ is

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$; focus $(3, 0)$.

If the focus of the parabola is $(3, -4)$ and the directrix is $y - 4 = 0,$ then the equation of the parabola is :-

If the distances of two points $P$ and $Q$ on the parabola $y^2 = 4ax$ from its focus are $4$ and $9$ respectively,then what is the distance of the point of intersection of the tangents at $P$ and $Q$ from the focus?