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Integer Answer Type Questions: Straight Lines and Pair of Straight Lines | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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Q.1. For a point P in the plane, let d1(P) a nd d2(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 ≤ d1 (P) + d2 (P)≤4 , is (JEE Adv. 2014)

Ans. (6)

Sol.  Let the point P be (x, y)

Then Integer Answer Type Questions: Straight Lines and Pair of Straight Lines | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEand Integer Answer Type Questions: Straight Lines and Pair of Straight Lines | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

For P lying in first quadrant x > 0, y > 0.
Also 2 ≤ d1(P) + d2(P) ≤ 4

Integer Answer Type Questions: Straight Lines and Pair of Straight Lines | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

If x > y, then  Integer Answer Type Questions: Straight Lines and Pair of Straight Lines | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

or Integer Answer Type Questions: Straight Lines and Pair of Straight Lines | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

If x < y, then

Integer Answer Type Questions: Straight Lines and Pair of Straight Lines | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEor Integer Answer Type Questions: Straight Lines and Pair of Straight Lines | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

The required region is the shaded region in the figure given below.

Integer Answer Type Questions: Straight Lines and Pair of Straight Lines | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ Required area =  Integer Answer Type Questions: Straight Lines and Pair of Straight Lines | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE = 8 – 2 = 6 sq units.

 

 

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