exam Maths Puzzle Numerical Ability

The radius of a circle defined by x^2+y^2-2x-4y+1=0

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Our problem is how to solve the following optimization problem:
Maximize x'Dx (with regard to x) subject to x'x=1, where D is a known symmetrical (n x n)-matrix and x is unknown ( A rectangle is twice as long as it is wide. If its length is decreased by 4 and its width is decreased by 2, its area is decreased by 32. Find the original dimensions.