A plane cutting the axes in P,Q,R passes...

A plane cutting the axes in P,Q,R passes through `(alpha,beta,beta-lambda,lambda-alpha)`. If O is origin, then locus of center of sphere OPQR is

`alphax+betay+lambdaz=4`

`(alpha-beta)x+(beta-lambda)y+(y-alpha)z=0`

`(alpha-beta)yz+(beta-y)zx+(lambda-alpha)xy=2xyz`

`(1/alpha^(2)+1/beta^(2)+1/lambda^(2))(x^(2+y^(2)+z^(2)))=xyz`

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