TS EAMCET · Maths · Straight Lines
Two points \(P(a, 2)\) and \(Q(1, b)\) lie on either side of the line \(2 x-3 y+1=0\). If \(P\) is the point of intersection of the lines \(4 x+3 y+k=0\) and \(3 x+4 y+k=0\), then the range of \(b\) is
- A \((-\infty, 3)\)
- B \((-\infty, 1)\)
- C \((1, \infty)\)
- D \(\quad(3, \infty)\)
Answer & Solution
Correct Answer
(B) \((-\infty, 1)\)
Step-by-step Solution
Detailed explanation
\(\because P\) and \(Q\) lie on either side of line \[ \begin{aligned} \therefore \quad & (2 a-3(2)+1)(2-3(b)+1) < 0 \\ & (2 a-5)(3-3 b) < 0 \\ & (2 a-5)(1-b) < 0 \end{aligned} \] Also \((a, 2)\) is point of intersection of \(4 x+3 y+k=0\) and…
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