Coordinate Geometry: JEE Main 2024 Mathematics question

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 :