Let the line \({L}_{1}:x+3=0\) intersect the lines \({L}_{2}:x-y=0\) and \({L}_{3}:3x+y=0\) at the points \(A\) and \(B,…

Let the line \({L}_{1}:x+3=0\) intersect the lines \({L}_{2}:x-y=0\) and \({L}_{3}:3x+y=0\) at the points \(A\) and \(B,\) respectively. Let the bisector of the obtuse angle between the lines \({L}_{2}\text{and}{L}_{3}\) intersect the line \({L}_{1}\) at the point \(C.\) Then \(B{C}^{2}:A{C}^{2}\) is equal to:

[JEE Main 2026, 4 Apr (Shift 1)]