If the straight line 2 x+3 y+1=0 bisects the angle between a pair of lines, one of which in this pair is 3 x+2 y+4=0 , then the equation of the other line in that pair of lines is

Step-by-step solution

Let the angle bisector of aligned & 3 x+2 y+4 and & y=m x+c is & 2 x+3 y+1=0 aligned Slope of line aligned & 3 x+2 y+4 is & m₁= -3 2 aligned Slope of line 2 x+3 y+1=0 is m₂= -2 3 Angle between lines and bisector are equal, aligned & so | m₂-m₁ 1+m₁ m₂ |= | m-m₂ 1+m₁ m₂ | & -2 / 3+3 / 2 1+1 = m+2 / 3 1- 2 m 3 5 12 = m+2 / 3 1-2 m / 3 & 5- 10 m 3 =12 m+8 ( 10 3 +12 ) m=-3 & 46 3 m=-3 m=- 9 46 aligned So, equation of required line is Now, for intersection point, equation 3 x+2 y+4=0 and 2 x+3 y+1=0 , is given by align