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JEE Main 202628 JanuaryEvening Shift
Exam
JEE Main
Year
2026
Date
28 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Ellipse

JEE Main 2026 · 28 January · Evening Shift · Mathematics · Ellipse

An ellipse has its center at (1,-2) , one focus at (3,-2) and one...

An ellipse has its center at (1,−2)(1,-2), one focus at (3,−2)(3,-2) and one vertex at (5,−2)(5,-2). Then the length of its latus rectum is :

Options

  1. A6
  2. B434 \sqrt{3}
  3. C163\frac{16}{\sqrt{3}}
  4. D636 \sqrt{3}

Correct answer

A. 6

Step-by-step solution

Center at (1,−2)(1, -2), focus at (3,−2)(3, -2), vertex at (5,−2)(5, -2) lie on horizontal line.
Distance from center to focus: c=2c = 2.
Distance from center to vertex: a=4a = 4.
Since b2=a2−c2=16−4=12b^2 = a^2 - c^2 = 16 - 4 = 12.
Length of latus rectum: L=2b2a=2(12)4=6L = \dfrac{2b^2}{a} = \dfrac{2(12)}{4} = 6
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