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P11 [Algebra] - Turkish NMO 1st Round - 2005

Source:

November 2, 2013
geometryinequalitiesanalytic geometrytriangle inequality

Problem Statement

For the real pairs (x,y)(x,y) satisfying the equation x2+y2+2x−6y=6x^2 + y^2 + 2x - 6y = 6, which of the following cannot be equal to (x−1)2+(y−2)2(x-1)^2 + (y-2)^2?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 9<spanclass=′latex−bold′>(C)</span> 16<spanclass=′latex−bold′>(D)</span> 23<spanclass=′latex−bold′>(E)</span> 30 <span class='latex-bold'>(A)</span>\ 2 \qquad<span class='latex-bold'>(B)</span>\ 9 \qquad<span class='latex-bold'>(C)</span>\ 16 \qquad<span class='latex-bold'>(D)</span>\ 23 \qquad<span class='latex-bold'>(E)</span>\ 30
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