The equation of the locus of all points equidistant from the point $(4, 2)$ and the $x$-axis is:

Tangent and normal are drawn at $P(16, 16)$ on the parabola ${y^2} = 16x$,which intersect the axis of the parabola at $A$ and $B$,respectively. If $C$ is the centre of the circle through the points $P, A$ and $B$ and $\angle CPB = \theta$,then a value of $\tan \theta$ is:

Let $O$ be the vertex and $Q$ be any point on the parabola $x^2=8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$,then the locus of $P$ is

If $A(at^2, 2at)$,$B(a/t^2, -2a/t)$,and $C(a, 0)$,then $2a$ is equal to

What is the equation of the chord of contact drawn from the point $(2, 4)$ to the parabola $y^2 = 4x$?

The point on the parabola $2y = x^2$ which is nearest to the point $(0, 3)$ is