Let \(P\left(x_0, y_0\right)\) be the point on the hyperbola \(3 x^2-4 y^2=36\), which is nearest to the line \(3 x+2 y=…

Let \(P\left(x_0, y_0\right)\) be the point on the hyperbola \(3 x^2-4 y^2=36\), which is nearest to the line \(3 x+2 y=1\). Then \(\sqrt{2}\left(y_0-x_0\right)\) is equal to:

[JEE Main 2023, 1 Feb (Shift 2)]