Question

The equation of the bisector of the acute angle between the lines $3 x - 4 y + 7 = 0$ and $12 x + 5 y - 2 = 0$ is

• A. $21 x + 77 y - 101 = 0$
• B. $11 x - 3 y + 9 = 0$
• C. $31 x + 77 y + 101 = 0$
• D. $11 x - 3 y - 9 = 0$

Answer 1

Answer: (B)

$11 x - 3 y + 9 = 0$

Answer 2

Bisector of the angles is given by $21 x + 77 y - 101 = 0$......(ii)

Let the angle between the line $3 x - 4 y + 7 = 0$ and (i) is $\alpha$ , then $\tan \alpha = \left| \frac { m _ { 1 } - m _ { 2 } } { 1 + m _ { 1 } m _ { 2 } } \right| = \left| \frac { \frac { 3 } { 4 } - \frac { 11 } { 3 } } { 1 + \frac { 3 } { 4 } \times \frac { 11 } { 3 } } \right| = \frac { 35 } { 45 } < 1 \Rightarrow \alpha < 45 ^ { \circ }$

Hence $11 x - 3 y + 9 = 0$ is the bisector of the acute angle between the given lines.