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 in S- lying inside the smaller part is

L:2x 3y 1,S:x^2+y^2 6 The shorter region lies in the non origin side of the line hence, L_1 0 nbsp; If L_1 0, S_1 0 , then the point lies in smaller part. ...

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Standard XII

Mathematics

Position of a Line with Respect to Circle

The straight ...

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 point(s) in $S,$ lying inside the smaller part is

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Solution

$L : 2 x - 3 y - 1, S : x^{2} + y^{2} - 6$

The shorter region lies in the non-origin side of the line hence, $L_{1} > 0$

If $L_{1} > 0, S_{1} < 0,$ then the point lies in smaller part.

$(2, \frac{3}{4}), (\frac{1}{4} . \frac{- 1}{4})$ satisfy both the conditions.
$∴$ there are two points in the smaller region.

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Similar questions

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 point(s) in

S,

lying inside the smaller part is

Q. Is the line through

(- 2, 3)

and

(4, 1)

perpendicular to the line

3 x = y + 1

? Does the line

3 x = y + 1

bisect the line joining of

(- 2, 3)

and

(4, 1) ?

Q. In what ratio the line joining the point

(2, 3) (4, 1)

divides the segment joining the point

(1, 2)

and

(4, 3)

Q. The point (4, 1) and (- 2, 4) are reflected in the line y = 3. Find the coordinates of their images.

Q. Determine whether the points are collinear.
(1) A(1, –3), B(2, –5), C(–4, 7)
(2) L(–2, 3), M(1, –3), N(5, 4)
(3) R(0, 3), D(2, 1), S(3, –1)
(4) P(–2, 3), Q(1, 2), R(4, 1)

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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 point(s) in S, lying inside the smaller part is

L:2x−3y−1,S:x2+y2−6 The shorter region lies in the non-origin side of the line hence, L1>0 If L1>0,S1<0, then the point lies in smaller part. (2,34),(14.−14) satisfy both the conditions. ∴ there are two points in the smaller region.

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 point(s) in $S,$ lying inside the smaller part is