Question

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

Answer 1

Write in the standard form of hyperbola `(y-k)^2/a^2-(x-h)^2/b^2 = 1`
The range will be `y >= k+ a` and `y <= k -a`
The domain is `x in RR`

Explanation:

Divide both sides if the given equation by 8:

`y^2/2^2-x^2/(2sqrt2)^2 = 1`

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

`y >= 2` and y <= -2

The domain is `x in RR`