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A triangle is formed by the lines x+y=0,...

A triangle is formed by the lines `x+y=0,x-y=0,` and `l x+m y=1.` If `l` and `m` vary subject to the condition `l^2+m^2=1,` then the locus of its circumcenter is (a) `(x^2-y^2)^2=x^2+y^2` (b) `(x^2+y^2)^2=(x^2-y^2)` (c) `(x^2+y^2)^2=4x^2y^2` (d) `(x^2-y^2)^2=(x^2+y^2)^2`

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