# What does the equation (x+2)^2/4-(y+1)^2/16=1 tell me about its hyperbola?

Jan 15, 2015

Quite a lot!

Here, we have the standard hyperbolic equation.

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

The center is at $\left(h , k\right)$

The semi-transverse axis is $a$

The semi-conjugate axis is $b$

The vertices of the graph are $\left(h + a , k\right)$ and $\left(h - a , k\right)$

The foci of the graph are $\left(h + a \cdot e , k\right)$ and $\left(h - a \cdot e , k\right)$

The directrices of the graph are $x = h + \frac{a}{e}$ and $x = h - \frac{a}{e}$

Here is an image to help.