JEE Main 2025 Jan 29 Shift 1, Physics Q17: Thin Lens and Mirrors

The thin-lens equation for a convex lens with real object and real image (sign convention with $u<0$ and $v>0$) can be rewritten as $(u+f)(v-f)=f^2.$

This is a rectangular hyperbola in the $(u,v)$-plane with asymptotes $u=-f$ and $v=f.$ For $|u|>f$ (real object beyond the focal point), $v$ is positive and finite: as $|u|\to f^{+}$, $v\to \infty$; as $|u|\to \infty$, $v\to f.$

Option (2) shows this monotonically decreasing hyperbolic branch with the two correct asymptotes.