# 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.