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Question 68 of 90
The area enclosed by the curve | x + 1 | + | y + 1 | = 2 is
1. 3 sq. umts
2. 4 sq. umts
3. 5 sq. umts
4. 8 sq. umts

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \\ \left|\mathrm{x}+1\right|+\left|\mathrm{y}+1\right|=2 \\ \mathrm{We} \mathrm{know} \mathrm{that} \\ \left|\mathrm{x}\right|+\left|\mathrm{y}\right|=\mathrm{a} \mathrm{is} \mathrm{a} \mathrm{square} \mathrm{with} \mathrm{side} \mathrm{length} \mathrm{a}\sqrt{2} \mathrm{unit} \mathrm{and} \mathrm{centre} \left(0,0\right) \\ \left[\mathrm{Hence} \mathrm{a}=2\right] \\ \mathrm{Now} \mathrm{if} \mathrm{centre} \mathrm{is} \mathrm{shifted} \mathrm{to} \left(-1,-1\right) \mathrm{the} \mathrm{equation} \mathrm{becomes} \\ \left|\mathrm{x}+1\right|+\left|\mathrm{y}+1\right|=\mathrm{a} \mathrm{which} \mathrm{means} \mathrm{only} \mathrm{origin} \mathrm{shifts} \mathrm{but} \mathrm{area} \mathrm{doesn}\text{'}\mathrm{t} \mathrm{change} \\ \mathrm{Now} \\ \mathrm{Area}={\left(\mathrm{side}\right)}^2={\left(\mathrm{a}\sqrt{2}\right)}^2=2{\mathrm{a}}^2=2\times 2^2=8 {\mathrm{unit}}^2 \end{gathered}$$

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