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JEE Advanced2011MathematicsCircleActual

The straight line 2 x-3 y=1 divides the circular region x^2+y^2 6 into two parts. If S= (2, 3 4 ), ( 5 2 , 3 4 ), ( 1 4 ,- 1 4 ), ( 1 8 , 1 4 ) , then the number of point(s) in S lying inside the smaller part is

Correct answer

2

Step-by-step solution

x^2+y^2 6 and 2 x-3 y=1 is shown as, For the point to lie in the shaded part, origin and the point lie on opposite side of straight line L . For any point in shaded part L>0 and for any point inside the circle S 0 and S: x^2+y^2-6 , S: 4+ 9 16 -6 0 ( 1 4 ,- 1 4 ) lies in the shaded part. For ( 1 8 , 1 4 ) L: 1 4 - 3 4 -1 < 0 [neglect] Only 2 points lie in the shaded part.

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