The diameter of the parabola $y^2 = 4ax$ which bisects the chords parallel to $y = mx + \alpha$ is:

If all the vertices of an equilateral triangle lie on the parabola $y^2=16x$ and one of them coincides with the vertex of that parabola,then the length of the side of that triangle is

If three real normals can be drawn from a point on the $x$-axis to the parabola $y^2 = 4ax$ $(a > 0)$,what is the range of the $x$-coordinate of the point?

Two parabolas have the same focus $(4, 3)$ and their directrices are the $x$-axis and the $y$-axis,respectively. If these parabolas intersect at the points $A$ and $B$,then $(AB)^2$ is equal to

The position of a moving point in the $XY$-plane at time $t$ is given by $\left( (u \cos \alpha)t, (u \sin \alpha)t - \frac{1}{2}gt^2 \right)$,where $u, \alpha, g$ are constants. The locus of the moving point is

If $x + y = k$ is a normal to the parabola $y^2 = 12x$,then what is the value of $k$?