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

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)=4x^(2)y^(2)`

D

`(x^(2)-y^(2))^(2)=(x^(2)+y^(2))^(2)`

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A
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