JEE Main 2022 · 27 Jun · Shift 2, Mathematics question 1

The curves. A circle with centre $(4,3)$ and radius 2, and an ellipse with foci $0$ and $4$ and major axis 6: centre $(2,0)$, $a=3$, $b^2=9-4=5$.

Position. The circle's lowest point $(4,1)$ is inside the ellipse ($\frac49+\frac15<1$), while its centre $(4,3)$ is outside. So the circle crosses the ellipse boundary twice (a numerical check confirms exactly two crossings).

(C)