Question

The locus of point of trisection of all the double ordinates of the parabola y square equal to lx is the parabola whose latus rectum is

Answer 1

Answer:

It seems that you think that the focuses of the both parabolas have the same $x$-coordinate.

The coordinates of the points both on the parabola $y^2=lx$and on $x=t$ are $(t,\pm\sqrt{lt})$

Since the double ordinates on $x=t$ are trisected, we get $\left(t,\frac{1\cdot\sqrt{lt}+2(-\sqrt{lt})}{1+2}\right)$,\quad \left(t,\frac{1\cdot(-\sqrt{lt})+2\cdot \sqrt{lt}}{1+2}\right)[/tex],$i.e. \left(t,\pm\frac{\sqrt{lt}}{3}\righ)[tex] which are on the parabola [tex] y^2=\frac{l}{3^\color{red}{2}}$x=$\frac{l}{9}x$