A triangle is formed by the lines x+y=0 and lx+my=1 . If l and m vary subject to the conditionl2+m2=1 , then the locus of its circum centre is

Coordinates of circum centre are l/(l2−m2),m/(m2−l2) .Henceh=ll2−m2...............(1)k=−ml2−m2...............(2)Squaring and adding (1) and (2) we geth2+k2=l2+m2(l2−m2)2=1(l2−m2)2 (putting l2+m2=1 )Hence, 1(l2−m2)2=(h2−k2)2Therefore, the locus is (x2−y2)2=x2+y2