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Q.1. For a point P in the plane, let d_{1}(P) a nd d_{2}(P) be the distance of the point P from the lines x – y = 0 and x + y = 0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2 ≤ d_{1} (P) + d_{2} (P)≤4 , is (JEE Adv. 2014)
Ans. (6)
Sol. Let the point P be (x, y)
Then and
For P lying in first quadrant x > 0, y > 0.
Also 2 ≤ d_{1}(P) + d_{2}(P) ≤ 4
If x > y, then
or
If x < y, then
or
The required region is the shaded region in the figure given below.
∴ Required area = = 8 – 2 = 6 sq units.
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