Let d 1(( x 1, y 1),( x 2, y 2))=| x 1- x 2|+| y 1- y 2| and d 2(( x 1, y 1),( x 2, y 2))=√( x 1- x 2)2+( y 1- y 2)2 denote the distance between (x1, y1) and (x2, y2) on the coordinate plane. The area of the region enclosed by the set of points ( x, y) satisfying d1((x, y),(0,0)) ≥ 1 and d2((x, y),(0,0)) ≤ 1, is

Question

Let d 1(( x 1, y 1),( x 2, y 2))=| x 1- x 2|+| y 1- y 2| and d 2(( x 1, y 1),( x 2, y 2))=√( x 1- x 2)2+( y 1- y 2)2 denote the distance between (x1, y1) and (x2, y2) on the coordinate plane. The area of the region enclosed by the set of points ( x, y) satisfying d1((x, y),(0,0)) ≥ 1 and d2((x, y),(0,0)) ≤ 1, is (A) π-2 (B) π+2 (C) π+4 (D) π-4

Tardigrade Admin · Accepted Answer

Clearly required area = Area of circle - Area of square =π-(√2)2=π-2 (square units)

$π - 2$

$π + 2$

$π + 4$

$π - 4$

Clearly required area $=$ Area of circle - Area of square $= π - (2)^{2} = π - 2$ (square units)

π−2

π+2

π+4

π−4

Clearly required area = Area of circle - Area of square =π−(2​)2=π−2 (square units)

$π - 2$

$π + 2$

$π + 4$

$π - 4$

Clearly required area $=$ Area of circle - Area of square $= π - (2)^{2} = π - 2$ (square units)