An elliptical running track has its two foci at (± 3, 0) on a plan whose lengths are in hundreds of…

Step 1. The semi-major axis. $c = 3$ and $e = \dfrac{c}{a} = \dfrac{3}{5}$, so $a = 5$.

Step 2. The semi-minor axis. $b^2 = a^2 - c^2 = 25 - 9 = 16$, so $b = 4$. The ellipse is $\dfrac{x^2}{25} + \dfrac{y^2}{16} = 1$.

Step 3. The latus rectum. $\dfrac{2b^2}{a} = \dfrac{32}{5} = 6.4$ hundred metres.