The length of the latus rectum of the ellipse, whose foci are (2,5) and (2,-3) and eccentr…

Question

The length of the latus rectum of the ellipse, whose foci are $(2,5)$ and $(2,-3)$ and eccentricity is $\dfrac45$, is:

Accepted Answer

Major axis is vertical (foci share $x=2$). $F_1F_2=8=2c\Rightarrow c=4$; with $e=\dfrac{c}{a}=\dfrac45$ (semi-major $a$), $a=5$.

$$b^2=a^2-c^2=25-16=9,\qquad \text{Latus rectum}=\frac{2b^2}{a}=\frac{18}{5}.$$

Solutions · 1