Let the system of equations : \(2x+3y+5z=9\\ 7x+3y-2z=8\\ 12x+3y-(4+\lambda )z=16-\mu ,\) have infinitely many solutions…

Let the system of equations :
\(2x+3y+5z=9\\ 7x+3y-2z=8\\ 12x+3y-(4+\lambda )z=16-\mu ,\)

have infinitely many solutions.

Then the radius of the circle centred at \((\lambda ,\mu )\) and touching the line \(4x=3y\) is

[JEE Main 2025, 7 Apr (Shift 1)]