Question

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

Answer 1

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.