ExamBro
ExamBro
AP EAMCET · Maths · Straight Lines

If the lines \(y=3 x+1\) and \(2 y=x+3\) are equally inclined to the line \(y=m x+4\), then the value of ' \(m\) ' is equal to

  1. A \(\frac{1 \pm 3 \sqrt{2}}{7}\)
  2. B \(\frac{-1 \pm 5 \sqrt{2}}{7}\)
  3. C 0
  4. D \(\frac{1 \pm 5 \sqrt{2}}{7}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1 \pm 5 \sqrt{2}}{7}\)

Step-by-step Solution

Detailed explanation

Given Lines are, \[ \begin{aligned} & y=3 x+1 \Rightarrow m_1=3 \Rightarrow 2 y=x+3 \\ & y=\frac{1}{2} x+\frac{3}{2} \Rightarrow m_2=\frac{1}{2} \\ & y=m x+4 \end{aligned} \] According to the question, \[ \left|\frac{m_1-m}{1+m_1 m}\right|=\left|\frac{m_2-m}{1+m_2 m}\right| \]…