Let \(\mathrm{P}\left({\mathrm{x}}_{0},{\mathrm{y}}_{0}\right)\) be the point on the hyperbola \(3{x}^{2}−4{y}^{2}\) = 3…

Let \(\mathrm{P}\left({\mathrm{x}}_{0},{\mathrm{y}}_{0}\right)\) be the point on the hyperbola \(3{x}^{2}−4{y}^{2}\) = 36 which is nearest to the line 3x + 2y = 1. Then \(\sqrt{2}\text{   }\left({y}_{0}−{x}_{0}\right)\) is equal to

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