The equation of the parabola whose vertex and focus are $(0, 4)$ and $(0, 2)$ respectively,is

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

From an external point $P(h, k)$,a pair of tangent lines are drawn to the parabola $y^2 = 4x$. If $\theta_1$ and $\theta_2$ are the inclinations of these tangents with the $x$-axis such that $\theta_1 + \theta_2 = \frac{\pi}{4}$,then the locus of $P$ is:

If $y = 2x - 3$ is a tangent to the parabola $y^2 = 4a(x - \frac{1}{3})$,then $a$ is equal to:

The slope of a chord of the parabola $y^2 = 4ax$ which is normal at one end and which subtends a right angle at the origin is