Ellipse
Ellipse from Given Centre, Focus, Vertex — Latus Rectum
nta_pyq_2026_jan
Grade 11
Question:
An ellipse has its centre at $(1,-2)$, one focus at $(3,-2)$ and one vertex at $(5,-2)$. Then the length of its latus rectum is:
6
$4\sqrt{3}$
$\dfrac{16}{\sqrt{3}}$
$6\sqrt{3}$
Step-by-Step Solution
Key Concept: Centre $(1,-2)$, focus $(3,-2)$: $c=2$. Vertex $(5,-2)$: $a=4$. $b^2=a^2-c^2=16-4=12$.
$a=4$, $b^2=12$. Latus rectum $=6$.
Correct Answer: 1