JEE Main 2026 (Online) 28th January Evening ShiftQuestion 1
An ellipse has its center at $(1,-2)$, one focus at $(3,-2)$ and one vertex at $(5,-2)$. Then the length of its latus rectum is :
Ellipse
Solution
Formulas used. (1) $c$ = centre to focus, $a$ = centre to vertex, $b^2=a^2-c^2$(2) Latus rectum $=\frac{2b^2}{a}$Step 1 - Use (1). Centre $(1,-2)$, focus $(3,-2)$: $c=2$. Vertex $(5,-2)$: $a=4$. Step 2 - Find $b^2$. $b^2=16-4=12$. Step 3 - Use (2). $\frac{2\cdot12}{4}=6$. Answer: C