Let a circle passing through (2,0) have its centre at the point ( h, k ). Let (x_c, y_c ) be the point of intersection of the lines 3 x+5 y=1 and (2+…

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