TS EAMCET · Maths · Pair of Lines
If the slopes of the lines represented by the equation \(6 x^2+2 h x y+4 y^2=0\) are in the ratio \(2: 3\), then the value of h such that both the lines make acute angles with the positive X -axis measured in positive direction is
- A 5
- B \(\frac{5}{2}\)
- C -5
- D \(-\frac{5}{2}\)
Answer & Solution
Correct Answer
(C) -5
Step-by-step Solution
Detailed explanation
\(m_1+m_2 = -\frac{2h}{4} = -\frac{h}{2}\) \(m_1 m_2 = \frac{6}{4} = \frac{3}{2}\) Let \(m_1 = 2k, m_2 = 3k\). Since slopes are positive, \(k>0\). \((2k)(3k) = \frac{3}{2} \Rightarrow 6k^2 = \frac{3}{2} \Rightarrow k^2 = \frac{1}{4} \Rightarrow k = \frac{1}{2}\)…
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