# How do you write the equation of each conic section ellipse with x-intercepts at (4, 0) and (-4, 0) and y-intercepts at (0, 1) and (0, -1)?

${\left(\frac{x}{4}\right)}^{2} + {\left(\frac{y}{1}\right)}^{2} = 1$, which can also be written as ${x}^{2} / 16 + {y}^{2} = 1$ or as ${x}^{2} + 16 {y}^{2} = 16$.
An equation of an ellipse with $x$-intercepts at $\left(\setminus \pm a , 0\right)$ and $y$-intercepts at $\left(0 , \pm b\right)$ can be written as ${\left(\frac{x}{a}\right)}^{2} + {\left(\frac{y}{b}\right)}^{2} = 1$, or ${x}^{2} / {a}^{2} + {y}^{2} / {b}^{2} = 1$.
You can see that this works by plugging in $y = 0$ and solving for $x$ and plugging in $x = 0$ and solving for $y$.