If from the origin a chord is drawn to the circle x2 + y2 - 2x = 0, then the locus of the mid point of the chord has equation

Let (h, k) be the mid point of the chord drawn through the origin. Then the equation of the chord is         hx+ky−(x+h)=h2+k2−2h              [Using : T=S']This passes through (0, 0).  ∴ −h=h2+k2−2h⇒h2+k2−h=0Hence, the locus of (h,k) is x2+y2−x=0