a variable circle cuts x-y axes so that the intercept are of given length k1 and k2. find the locus of centre of circle

Let the eqn of circle be x^2+y^2+2gx+2fy+c=0 , given x intercept =k1 then,2(g^2-c)^1÷2 =k1 similarly y intercept=k2=2(f^2-c)^1÷2 eliminate c by squaring and replace g by x and f by y to get the locus which equals x^2-y^2=1/4(k1^2-k2^2)