# How do I graph (x+2)^2/9+(y-3)^2/25=1 algebraically?

Oct 8, 2014

You have an ellipse in the form

${\left(x - h\right)}^{2} / {b}^{2} + {\left(y - k\right)}^{2} / {a}^{2} = 1$

where (h, k) is the ellipse's center.
You have $\left(- 2 , 3\right)$ as your center.

$a$ is under $y$. That means your major axis is vertical with length $2 a = 10$.
The endpoints of your major axis are $\left(- 2 , - 2\right)$ and $\left(- 2 , 8\right)$

Meanwhile, the minor axis is horizontal with length $2 b = 6$
The endpoints of your major axis are $\left(- 5 , 3\right)$ and $\left(1 , 3\right)$

Connect the endpoints of your major and minor axis and you have your ellipse