JEE Math Practice 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 :

1. A.$$5 x^2+5 y^2-4 x-2 y-12=0$$
2. B.$$25 x^2+25 y^2-20 x+2 y-60=0$$
3. C.$$25 x^2+25 y^2-2 x+2 y-60=0$$
4. D.$$5 x^2+5 y^2-4 x+2 y-12=0$$