TS EAMCET · Maths · Pair of Lines
Let \(P\) be the pair of lines represented by \(2 x^2-5 x y+2 y^2+6 x-3 y=0\) and consider the following independent statements (i) \(\alpha\) is the \(x\) coordinate of the point of intersection of the pair of lines \(P\). (ii) \(\beta\) is the slope of one of the lines of \(P\) passing through origin. (iii) \(\gamma\) is the constant term in the equation of the pair of angular bisectors of \(P\). Then,
- A \(\beta < \gamma < \alpha\)
- B \(\alpha < \beta=\gamma\)
- C \(\alpha=\beta < \gamma\)
- D \(\gamma < \alpha < \beta\)
Answer & Solution
Correct Answer
(D) \(\gamma < \alpha < \beta\)
Step-by-step Solution
Detailed explanation
Given pairs of lines \(2 x^2-5 x y+2 y^2+6 x-3 y=0\) \(\Rightarrow \quad(2 y-x-3)(y-2 x)=0\) \(\therefore\) Pairs of line are \(2 y-x-3=0 \text { and } y-2 x=0\) Solving these equation we get, \(x=1, y=2\) \(\therefore \quad \alpha=1\) Equation of line passing through origin is…
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