# How do you find the center and vertices and sketch the hyperbola y^2/1-x^2/4=1?

Mar 28, 2018

Write your equation in form: ${\left(y - {y}_{c}\right)}^{2} / {a}^{2} - {\left(x - {x}_{c}\right)}^{2} / {b}^{2} = 1$
where the center is $C = \left({x}_{c} , {y}_{c}\right)$

#### Explanation:

Center: $C = \left(0 , 0\right)$, $a = 1$, $b = 2$
Draw a rectangle $2 b$ width and $2 a$ length.
[Alternative: draw $x = - 2$ , $x = 2$, $y = 1$, $y = - 1$ (green lines)]
So you know hyperbola have the vertices at $\left(0 , - 2\right)$ and $\left(0 , 2\right)$ and is "going towards" the asymtotes.