Question

What is the equation of the ellipse with vertices at (-25, 0), (25, 0) and co-vertices (0, -15), (0, 15)?

Answer 1

Check the picture below.

$\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ a=25\\ b=15 \end{cases}\implies \cfrac{(x-0)^2}{25^2}+\cfrac{(y-0)^2}{15^2}=1\implies \cfrac{x^2}{625}+\cfrac{y^2}{225}=1$