The locus of the middle point of chords of the circle x2+y2=a2 which pass through the fixed point (h, k), is

Let (α, β) be the mid point of a chord of the circle x2+y2=a2. Then its equation is    αx+βy=α2+β2                                              [Using S=T]This passes through (h, k).∴ αh+βk=α2+β2Hence, the locus of (α, β) isx2+y2=hx+ky⇒x2+y2−hx−ky=0.