Circle

Let a circle passing through \((2,0)\) have its centre at the point \((\mathrm{h}, \mathrm{k})\). Let \((x_{\mathrm{c}}, y_{\mathrm{c}})\) be the point of intersection of the lines \(3 x+5 y=1\) and \((2+\mathrm{c}) x+5 \mathrm{c}^2 y=1\). If \(\mathrm{h}=\lim _\limits{\mathrm{c} \rightarrow 1} x_{\mathrm{c}}\) and \(\mathrm{k}=\lim _\limits{\mathrm{c} \rightarrow 1} y_{\mathrm{c}}\), then the equation of the circle is :