Question

A straight line passes through a fixed point $(h,k)$. Find the locus of feet of the perpendiculars, drawn from the origin to it.

Answer 1

$y-k=m(x-h)$ where $m$ is parameter.....(1)
Equation of the line through $(0,0)$ perpendicular to (1) is
$y=(-1/m)x.....\left(2\right)$
Foot of perpendicular is intersection of (1) and (2) and its locus is obtained by eliminating $m$
$y-k=-\frac{x}{y}(x-h)$
or $x^2+y^2-hx-ky=0$