<s>[INST] How to get the foci / focus Hyperbola How to find the lower and upper focus? Hyperbola 
I started with this
$$ 9x^2 + 54x - y^2 + 10y + 81 = 0 $$
and broke it down to
$$ \frac{9(x+3)^2}{25} - \frac{(y-5)^2}{25} = -1 $$
center = (-3,5) 
Lower Vertex = (-3,0)
Upper Vertex = (-3,10)
How to get the foci? 
foci / focus =  (h, k +- c)
b = 5 but what is a?
$$ c^2 = a^2 + b^2  $$
Thank you.
 [/INST] We have $a^2=\frac{25}{9}$ because we have
$$\frac{(x+3)^2}{\dfrac{25}{9}}-\frac{(y-5)^2}{25}=-1.$$

The foci of a hyperbola
$$\frac{(x-m)^2}{a^2}-\frac{(y-n)^2}{b^2}=-1$$
are
$$\left(m,n\pm\sqrt{a^2+b^2}\right).$$
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