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JEE Main202628 January 2026Evening ShiftMathematicsEllipseActual

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 :

Options

  1. A6
  2. B4 3
  3. C16 3
  4. D6 3

Correct 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

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