The locus of feet of perpendiculars drawn from origin to the straight lines passing through (2,  1) is

$\begin{array}{l}Letp(x,y)bethepo\mathrm{int}onlocus\\ GivenA(2,1)andO(0,0)\\ {\Delta }^{le}OPAisRightangle{\Delta }^{le}\\ \therefore P{A}^2+P{O}^2=O{A}^2\\ \Rightarrow {(x-2)}^2+{(y-1)}^2+x^2+y^2=4+1\\ \Rightarrow x^2+4-4x+y^2+1-2y+x^2+y^2=4+1\\ \Rightarrow 2x^2+2y^2-4x-2y=0\\ \Rightarrow x^2+y^2-2x-y=0\end{array}$