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 points(s) in S lying inside the smaller part is [

Question

The straight line $2 x - 3 y = 1$ divides the circular region $x^{2} + y^{2} \leq 6$ into two parts.

If $S = {(2, \frac{3}{4}), (\frac{5}{2}, \frac{3}{4}), (\frac{1}{4}, - \frac{1}{4}), (\frac{1}{8}, \frac{1}{4})}$ , then the number of points(s) in S lying inside the smaller part is [2011]

Smart Achievers · Accepted Answer

(2)

The smaller region of circle is the region given by

$x^{2} + y^{2} \leq 6 ...(i)$

and $2 x - 3 y \geq 1 ...(ii)$

We observe that only two points $(2, \frac{3}{4})$ and $(\frac{1}{4}, - \frac{1}{4})$ satisfy both the inequalities (i) and (ii).

$∴$ $2 points in S lie inside the smaller part.$

Solution

Q.
The straight line $2 x - 3 y = 1$ divides the circular region $x^{2} + y^{2} \leq 6$ into two parts.

If $S = {(2, \frac{3}{4}), (\frac{5}{2}, \frac{3}{4}), (\frac{1}{4}, - \frac{1}{4}), (\frac{1}{8}, \frac{1}{4})}$ , then the number of points(s) in S lying inside the smaller part is [2011]

Want Us to Email you About Special Offers & Updates?

Solution

Q. The straight line 2x-3y=1 divides the circular region x2+y2≤6 into two parts. If S={(2,34),(52,34),(14,-14),(18,14)}, then the number of points(s) in S lying inside the smaller part is [2011]

Ans. (2) The smaller region of circle is the region given by x2+y2≤6 ...(i) and 2x-3y≥1 ...(ii) We observe that only two points (2,34) and (14,-14) satisfy both the inequalities (i) and (ii). ∴ 2 points in S lie inside the smaller part.

Want Us to Email you About Special Offers & Updates?

Q.
The straight line $2 x - 3 y = 1$ divides the circular region $x^{2} + y^{2} \leq 6$ into two parts.

If $S = {(2, \frac{3}{4}), (\frac{5}{2}, \frac{3}{4}), (\frac{1}{4}, - \frac{1}{4}), (\frac{1}{8}, \frac{1}{4})}$ , then the number of points(s) in S lying inside the smaller part is [2011]