Area of the region defined by $1 \leq |x| + |y|$ and $x^{2} - 2 x + 1 \leq 1 - y^{2}$ is $kπ$ then k =

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$\frac{3}{4}$

$\frac{7}{6}$

$\frac{128}{5}$

$\frac{10}{3}$

answer is A.

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Detailed Solution

$x^{2} - 2 x + 1 \leq 1 - y^{2}$

$\Rightarrow {(x - 1)}^{2} + y^{2} \leq 1$

Represents a circle with centre (1,0)

Required area = area of circle- area of sector ABC= $π {(1)}^{2} - \frac{1}{2} {(1)}^{2} \frac{π}{2} = π - \frac{π}{4} = \frac{3 π}{4}$

$k π = \frac{3 π}{4} \Rightarrow k = \frac{3}{4}$

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