Question

Find the center, vertices, and foci of the ellipse with equation x squared divided by 16 plus y squared divided by 25 = 1.

Answer 1

`\bf \cfrac{(x-{{ h}})^2}{{{ b}}^2}+\cfrac{(y-{{ k}})^2}{{{ a}}^2}=1 \qquad \begin{array}{llll} center\ ({{ h}},{{ k}})\\\\ vertices\ ({{ h}}, {{ k}}\pm a)\\\\ foci\ (h\ ,\ k\pm √(a^2-b^2)) \end{array} \\\\ -----------------------------\\\\ \cfrac{x^2}{16}+\cfrac{y^2}{25}=1\implies \cfrac{(x-0)^2}{4^2}+\cfrac{(y-0)^2}{5^2}=1`

in an ellipse, the "a" component, is always the bigger denominator, in this case the 5, which is under the "y", meaning the "y-axis" is the major axis, and thus the foci are
`c=√(a^2-b^2)` distance from "k" coordinate

Answer 2

Center: (0,0)

Vertices: (0,-5), (0,5)

Foci: (0,-3) (0,3)