The line $3 x - 3 y + 17 = 0$ bisects the angle between a pair of lines, where one line is $2 x + y + 4 = 0$ , then the equation of the other line is

3 x + 6 y - 5 = 0

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3 x + 6 y - 7 = 0

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7 x - y + 14 = 0

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4 x - y + 3 = 0

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Solution

The correct option is A $3 x + 6 y - 5 = 0$
Following the figure, we get
$tan θ = ∣ ∣ ∣ \frac{m_{2} - m_{1}}{1 + m_{1} m_{2}} ∣ ∣ ∣ = ∣ ∣ ∣ \frac{3}{- 1} ∣ ∣ ∣ = 3$
And similarly
$tan θ = ∣ ∣ ∣ \frac{m_{1} - m}{1 + m m_{1}} ∣ ∣ ∣ = ∣ ∣ ∣ \frac{1 - m}{1 + m} ∣ ∣ ∣ = 3$

$\Rightarrow 1 - m = 3 (1 + m)$ or $m - 1 = 3 (1 - m)$
$\Rightarrow - 2 = 4 m$ or $2 m = - 4$
$m = - \frac{1}{2}$ or $m = - 2$
So, equation of line having slope $- \frac{1}{2}$ and passing through $(- \frac{29}{3}, - 4)$ is
$\Rightarrow 3 x + 6 y - 5 = 0$

Hence, option A

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