Question

Find the equation of the ellipse with the following properties.

The ellipse with x-intercepts (5, 0) and (-5, 0); y-intercepts (0, 3) and (0, -3).

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 √( a ^2- b ^2) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=0\\ k=0\\ a=5\\ b=3 \end{cases}\implies \cfrac{(x-0)^2}{5^2}+\cfrac{(y-0)^2}{3^2}=1\implies \cfrac{x^2}{25}+\cfrac{y^2}{9}=1`