A metal plate is cut along the curve 9x² + 16y² = 144, with lengths in centimetres…

Step 1. Standard form. $\dfrac{x^2}{16} + \dfrac{y^2}{9} = 1$, so $a = 4$ and $b = 3$.

Step 2. The focus. $c = \sqrt{16 - 9} = \sqrt{7} \approx 2.646$ centimetres.

Step 3. The eccentricity. $e = \dfrac{\sqrt{7}}{4} \approx 0.661$.

Step 4. The latus rectum. $\dfrac{2 \times 9}{4} = 4.5$ centimetres. The directrix is at $x = \dfrac{a}{e} = \dfrac{16}{\sqrt{7}} \approx 6.05$ centimetres.