Question 1184206
Let (x', y') be the midpoint of the chord joining (0,0) to (x, {{{2sqrt(2x)}}}) (or (x, {{{-2sqrt(2x)}}})), which is a point on the parabola {{{ y^2 = 8x}}}.


===> (x',y') = (x/2, {{{sqrt(2x)}}})


===> y' = {{{sqrt(4*(x/2)) = 2sqrt(x/2)}}} = 2√x'

===> (y')^2 = 4x'.


Therefore, the locus of the point P is the equation {{{y^2 = 4x}}}.