Let the plane \(P: 8 x+\alpha_1 y+\alpha_2 z+12=0\) be parallel to the line \(L: \frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{…

Let the plane \(P: 8 x+\alpha_1 y+\alpha_2 z+12=0\) be parallel to the line \(L: \frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}\). If the intercept of \(P\) on the \(y\)-axis is 1 , then the distance between \(P\) and \(L\) is:

[JEE Main 2023, 31 Jan (Shift 2)]