# How do you find the center, foci and vertices of the hyperbola (x-1)^2/4-(y+2)^2/1=1?

Apr 21, 2018

#### Explanation:

consider the equation to be:

${\left(x - h\right)}^{2} / {a}^{2} - {\left(y - k\right)}^{2} / {b}^{2} = 1$

is an equation of a horizontal hyperbola

$a = 2$ $\text{ , }$$b = 1$

${b}^{2} = {a}^{2} \left({e}^{2} - 1\right)$$\rightarrow$ $e = \frac{\sqrt{5}}{2}$

it's center is $\left(h , k\right) \rightarrow \left(1 , - 2\right)$

it's foci are $\left(h \pm a e , k\right) \rightarrow \left(1 \pm \sqrt{5} , - 2\right)$

its vertices are $\left(h \pm a , k\right) \rightarrow \left(1 \pm 2 , - 2\right)$