Question

If the lines $2y = x + 3$ and $y = 3x + 1$ are equally inclined to the line, $y = mx + 4$, then the value of $m$ is

• A. $\frac{1\pm5\sqrt{2}}{7}$
• B. $\frac{5\sqrt{2}-1}{7}$
• C. $\frac{1-5\sqrt{2}}{5}$
• D. None of these

Answer 1

Answer: (A)

We have,
$\frac{m-m_{1}}{1+m_{1}m}=\frac{m_{2}-m}{1+mm_{2}}$
$\Rightarrow \frac{m-3}{1+3m}=-\frac{\left(2m-1\right)}{m+2}$
$\Rightarrow \left(m - 3\right) \left(m + 2\right) + \left(2m - 1\right) \left(1 + 3m\right) = 0$
$\Rightarrow 7m^{2}-2m-7=0$
$\Rightarrow m=\frac{1\pm5\sqrt{2}}{7}$