JEE Main 2024 — Circle Question with Solution

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 $$3x+5y=1$$ 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 :