\({x}^{2}+{y}^{2}-\alpha x-\beta y+\gamma =0\), this circle touches \(x\) axis at \((a,0)\) and it's \(Y\) intercept is …

\({x}^{2}+{y}^{2}-\alpha x-\beta y+\gamma =0\), this circle touches \(x\) axis at \((a,0)\) and it's \(Y\) intercept is \(b\). Find \(\left(2a,{b}^{2}\right)\) in terms of \(\alpha ,\beta ,\gamma\). (28 Jan, Shift I, Memory Based)