A = ( 1 , − 2 ) and B = ( − 3 , 2 ) are fixed vertices on the circumcircle x 2 + y 2 + 3 x + y − 6 = 0 of △ A BC . As C varies on this circle, the orthocentre of △ A BC traces a

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With fixed circumcentre O = ( − 3/2 , − 1/2 ) , the orthocentre is H = A + B + C − 2 O = C + ( 1 , 1 ) . As C moves on the given circle, H traces a translate of it, which is again a circle.

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