An ellipse has its centre at (1,-2), one focus at (3,-2), and one vertex at (5,-2).

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:

Accepted Answer

The centre, focus and vertex share $y=-2$, so the major axis is horizontal.

$$a=|5-1|=4,\qquad c=|3-1|=2.$$

$b^2=a^2-c^2=16-4=12.$

$$\text{Latus rectum}=\frac{2b^2}{a}=\frac{2\times12}{4}=6.$$

Solutions · 1