Question

Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 10.

Answer 1

x^2/25 + y^2/81 =1

Explanation:

solved it

Answer 2

`\bf \textit{ellipse, vertical major axis}\\\\ \cfrac{(x-{{ h}})^2}{{{ b}}^2}+\cfrac{(y-{{ k}})^2}{{{ a}}^2}=1 \qquad \begin{cases} center\ ({{ h}},{{ k}})\\ vertices\ ({{ h}}, {{ k}}\pm a)\\ \textit{major axis}\ a+a=18\\ \qquad 2a=18\implies \boxed{a=9}\\ \textit{minor axis}\ b+b=10\\ \qquad 2b=10\implies \boxed{b=5} \end{cases} \\\\\\ \begin{cases} h=0\\ k=0\\ a=9\\ b=5 \end{cases}\implies \cfrac{x^2}{5^2}+\cfrac{y^2}{9^2}=1`

check the picture below.