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Question 5

The area of the curve enclosed by $$|x-2\sqrt{2}|+|y-\sqrt{5}|=2$$ is

Solution

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Translating the centre does not change the area, so consider $$|x|+|y|=2$$. This is a rhombus with diagonals $$4$$ and $$4$$. Its area is $$\frac{1}{2}\times4\times4=8$$.

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