First slide

Equation of line in Straight lines

Question

If the lines $3 x - y + 1 = 0$ and $x - 2 y + 3 = 0$ are equally inclined to the line $y = m x$ , then the value of m is given by

Moderate

A

$2 m^{2} - 7 m - 7 = 0$
B

$7 m^{2} - 7 m - 7 = 0$
C

$7 m^{2} - 2 m - 7 = 0$
D

$2 m^{2} - 7 m - 2 = 0$

Solution

It $θ$ is the angle between the lines then $\tan θ = |\frac{m - 3}{1 + 3 m}| = |\frac{m - (1 / 2)}{1 + m (1 / 2)}|$
$\begin{array}{l} \Rightarrow (m - 3) (2 + m) = \pm (2 m - 1) (3 m + 1) \\ \Rightarrow m^{2} - m - 6 = \pm (6 m^{2} - m - 1) \end{array}$
$\Rightarrow 7 m^{2} - 2 m - 7 = 0 o r m^{2} + 1 = 0$

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