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

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Answer 1 · 2015-01-15T03:46:27

Quite a lot!

Here, we have the standard hyperbolic equation.

$(x-h)^2/a^2-(y-k)^2/b^2=1$

The center is at $(h,k)$

The semi-transverse axis is $a$

The semi-conjugate axis is $b$

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

The foci of the graph are $(h+a*e, k)$ and $(h-a*e, k)$

The directrices of the graph are $x = h + a/e$ and $x = h - a/e$

Here is an image to help.

![http://formulas.tutorvista.com/math/http://hyperbola-formula.html](https://useruploads.socratic.org/YoUuy4cRSPCSUsRxTE0i_hyperbola.png)

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