JEE Main · 2026 · 28 Jan 2026 · Shift 2 · Ellipse

The centre $(1,-2)$, focus $(3,-2)$ and vertex $(5,-2)$ all lie on $y=-2$, so the major axis is horizontal. The semi-major axis is $a=|5-1|=4$ and the centre-to-focus distance is $ae=|3-1|=2$, giving $e=\frac{1}{2}$. Then $b^2=a^2(1-e^2)=16\left(1-\frac{1}{4}\right)=12$. The length of the latus rectum is

The length of the latus rectum is $6$.