If P(1,0),Q(−1,0) and R(2,0) are three given points, then the locus of point S satisfying the relation SQ2+SR2=2SP2, is

Let the coordinates of S be (h, k). Then, SQ2⋅SR−=2SP2⇒ (h+1)2+k2+(h−2)2+k2=2(h−1)2+k2−2h+5=−4h+2⇒ 2h+3=0 Hence, locus of  (h,k)  is, 2x+3=0 which is a straight line parallel to y-axis.