The locus of midpoint of focal chords of the parabola ${\mathrm{y}}^2=4\mathrm{ax}$ is

$\begin{array}{l}Given parabola y^2=4ax\\ let P(x_1,y_1) be locus of mid point\\ Equation of chord is S_1=S_{11}\\ y{y}_1-2a(x+x_1)={y^2}_1-4a{x}_1\\ it passes through (a,0) then\\ {y_1}^2=2ax-2a^2\\ locus is y^2=2a(x-a)\\ \Rightarrow {\mathrm{y}}^2=2\mathrm{a}(\mathrm{x}-\mathrm{a})\end{array}$