# How do you find the domain and range of 2y^2-x^2 = 8?

Oct 21, 2017

#### Answer:

Write in the standard form of hyperbola ${\left(y - k\right)}^{2} / {a}^{2} - {\left(x - h\right)}^{2} / {b}^{2} = 1$
The range will be $y \ge k + a$ and $y \le k - a$
The domain is $x \in \mathbb{R}$

#### Explanation:

Divide both sides if the given equation by 8:

${y}^{2} / {2}^{2} - {x}^{2} / {\left(2 \sqrt{2}\right)}^{2} = 1$

Please observe that $k = 0$, therefore, the range is:

$y \ge 2$ and y <= -2

The domain is $x \in \mathbb{R}$