Answer:
Option C
Explanation:
Plan Distance of a point (x1,y1) from ax+bx+c=0 is given by
|ax1+by1+c√a2+b2|

Let P(x,y) is the point in first quadrant.
Now, 2≤|x−y√2|+|x+y√2|≤4
2√2≤|x−y|+|x+y|≤4√2
Case I x≥y
2√2≤(x−y)+(x+y)≤4√2
⇒ x∈(√2,2√2)
Case II x<y
2√2≤y−x+(x+y)≤4√2
y∈(√2,2√2)
⇒ A=(2√2)2−(√2)2=6