Question

Write an equation of an ellipse in standard form with the center at the origin and with the given characteristics.

Answer 1

Check the picture below.

$\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ a=3\\ b=2 \end{cases}\implies \cfrac{(x- 0)^2}{ 3^2}+\cfrac{(y- 0)^2}{ 2^2}=1\implies \cfrac{x^2}{9}+\cfrac{y^2}{4}=1$