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PQRS is a square of side 'b'. Prove that...

PQRS is a square of side 'b'. Prove that the equation of circumcircle of square PQRS, where PQ and PS are the axes, is `x^(2)+y^(2)=b(x+y)`.

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Draw a square of side 'b' taking PS as the axes. Now the co-ordinates of its vertices are `P(0,0), Q(b,0),R(b,b) and S(0,b)`
From the equation of circumcircle of square PQRS,
`(x_(1),y_(1))=(0,0) and (x_(2),y_(2))=(b,b)`
Equation of circle
`(x-x_(1))(x-x_(2))+(y-y_(1))(y-y_(2))=0`
`rArr (x-0)(x+b)+(y-0)(y-b)=0`
`rArr x^(2) -bx + y^(2) -by =0`
`rArr x^(2) +y^(2)=b(x+y)`.
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