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JEE Advanced 2014Paper 1
Exam
JEE Advanced
Year
2014
Paper
Paper 1
Subject
Mathematics
Chapter
Straight Lines

JEE Advanced 2014 · Paper 1 · Mathematics · Straight Lines

For a point P in the plane, let d _ 1 (P) and d _ 2 (P) be the...

For a point P in the plane, let d1(P){d}_{1}\left(P\right) and d2(P){d}_{2}\left(P\right) be the distances of the point P from the lines x−y=0x - y = 0 and x+y=0x + 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≤d1(P)+d2(P)≤4,2 \le {d}_{1}\left(P\right) + {d}_{2}\left(P\right) \le 4, is ________For a point P in the plane, let d _ 1 (P) and d _ 2 (P) be the distances of the point P from the lines x - y = 0 and x

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Step-by-step solution


For a point P in the plane, let d _ 1 (P) and d _ 2 (P) be the distances of the point P from the lines x - y = 0 and x
2≤d1(p)+d2(p)≤42 \le {d}_{1}\left(p\right) + {d}_{2}\left(p\right) \le 4
For P(α,β),α>βP\left(\alpha, \beta\right), \alpha > \beta
⇒⇒ 22≤2α≤422\sqrt{2} \le 2\alpha \le 4\sqrt{2}
2≤α≤22\sqrt{2} \le \alpha \le 2\sqrt{2}
⇒⇒ Area of region =((22)2−(2)2)= \left({\left(2\sqrt{2}\right)}^{2} - {\left(\sqrt{2}\right)}^{2}\right)
=8−2=6sq.units= 8 - 2 = 6sq . units
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