Question
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 :
JEE Main
Mathematics
Ellipse
2026
JEE Main 2026 (28 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 6
- B. 4 3
- C. 16 3
- D. 6 3
Answer
A. 6
Step-by-step solution
Center at (1, -2), focus at (3, -2), vertex at (5, -2) lie on horizontal line. Distance from center to focus: c = 2. Distance from center to vertex: a = 4. Since b^2 = a^2 - c^2 = 16 - 4 = 12. Length of latus rectum: L = 2b^2 a = 2(12) 4 = 6
Related: Mathematics — Ellipse · All PYQ Banks