Let \(L\) be a tangent line to the parabola \(y^2=4 x-20\) at \((6,2)\). If \(L\) is also a tangent to the ellipse \(\fr…

Let \(L\) be a tangent line to the parabola \(y^2=4 x-20\) at \((6,2)\). If \(L\) is also a tangent to the ellipse \(\frac{x^2}{2}+\frac{y^2}{b}=1\), then the value of \(b\) is equal to:

[JEE Main 2021, 17 Mar (Shift 2)]