The locus of the middle points of chords of the circle x2+y2=25  which are  parallel to the line    x−2y+3=0 is

Let (h,k)   be the mid-point of a chord of the circlex2+y2=25 Then, equation of the chord ishx+ky−25=h2+k2−25⇒hx+ky=h2+k2If this is parallel to x−2y+3=0, then −hk=12⇒2h+k=0So, the locus of  (h,k) is   2x+y=0