A point P is taken with coordinates of (x,y), the according to condition. PA2+PB2=2PC2 (x−2)2+(y−3)2+(x−3)2+(y+6)2= 2[(x−5)2+(y+7)2] On solving the above expression we get, 10x−22y=90 By going though options, the points became (-13,-10) which lies on the locus of P.