Straight Lines and Pair of Straight Lines

Let the slope of other line be m.
Now, point of intersection of the line 2x+3y+1=0 and 3x+2y+4=0 is x=−2 and y=1
Now, the 2x+3y+1=0 makes equal angle to the line 3x+2y+4=0 and other line.
‌

m+ 2 3

1−‌ 2m 3

‌=‌

‌ 3 2 − 2 3

1+‌ 3 2 ⋅‌ 2 3

⇒‌‌‌

3m+2

3−2m

‌=‌

5

12

Solving this, we get m=−‌

9

46

∵ Equation of other line
‌Y−1=−‌

9

46

(x+2
⇒46y−46=−9x−18
⇒9x+46y−28=0