JEE Main 2026 — Jan 28, Shift 2 — Mathematics solution

JEE Main2026Jan 28, Shift 2Mathematics

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 :

Solution

All three points lie on the horizontal line $y = - 2$ , so the major axis is horizontal.

Semi-major axis: $a =$ distance from center to vertex $= ∣5 - 1∣ = 4$ .

Focal distance: $a e = ∣3 - 1∣ = 2 \Rightarrow e = \frac{1}{2}$ .

$b^{2} = a^{2} (1 - e^{2}) = 16 \cdot \frac{3}{4} = 12$ .

Length of latus rectum $= \frac{2 b ^{2}}{a} = \frac{24}{4} = 6$ .

Practice more Mathematics

Concept-wise practice with instant solutions on Fundamenthol.