COORDINATE GEOMETRY

let the point is (h,k)   so   { slope of line joining (h,k) and (-5,1) } * { slope of line joining (h,k) and (3,2) }  = -1

slope of line joining (h,k) and (-5,1) = (k-1) / (h+5)

slope of line joining (h,k) and (3,2)  =  (k-2) / (h-3)

so  (k-1) (k-2) / (h+5) (h-3)  = -1  by solving we get locus is a circle x² + y²+2x - 3y - 13= 0