How to find the equation of a Hyperbola?

Find the equation of a hyperbola with following characteristics.

$Origin: (0,0)\ Focus: (3,0)\ Vertex: (-2,0)$

a is the distance from the origin of the hyperbola c is the distance from the origin to the foci $ foci = (3,0), (-3,0) $

$ a = 2 $ $ c = 3 $ ${b}^{2} = {c}^{2}-{a}^{2}$ ${b}^{2} = {3}^{2}-{2}^{2}$ ${b}^{2} = 9-4$ ${b}^{2} = 5$

Remember the standard form of an Hyperbola?

$\frac { { x }^{ 2 } }{4} -\frac { { y }^{ 2 } }{ 5 } =1$

Now the last part remaing is to plot two points on the graph. Just use $\pm 3$ In the function.