Problem

The locus of the mid-point of the focal radii of a variable point moving on the parabola

y^2 = 4ax

is a parabola whose a. latusrectum is half the latusrectum of the original parabola b. vertex is

\left(\frac{a}{2}, 0\right)

c. directrix is Y-axis d. focus has the coordinates

(a, 0)