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A clrcle whose centre lies on the hyperbola (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1intersects the rectangular hyperboal xy = c ^(2) in four points. Show that the locus of the centre of the locus of the centroid of triangle formed by any three points of intersectivon is (x ^(2))/(a^(2)) - (y ^(2))/(b ^(2)) = ((2)/(3)) ^(2). |
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