The straight line 2x-3y = 1 divides the circular region `x^2+ y^2 le6` 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

Explanation

To solve the problem, we need to determine how many points from the set \( S = \{ (2, \frac{3}{4}), (\frac{5}{2}, \frac{3}{4}), (\frac{1}{4}, -\frac{1}{4}), (\frac{1}{8}, \frac{1}{4}) \} \) lie inside the smaller region created by the line \( 2x - 3y = 1 \) and the circle defined by \( x^2 + y^2 \leq 6 \).

### Step 1: Analyze the Circle
The equation of the circle is given by:
\[ x^2 + y^2 = 6 \]
This represents a circle centered at the origin (0,0) with a radius of \( \sqrt{6} \).
...