How do you find the center and vertices and sketch the hyperbola y^2/9-x^2/1=1?

Jan 6, 2017

Explanation:

The center of a hyperbola with an equation of the general form:

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

is the point $\left(h , k\right)$

In the given equation, h and k are obviously 0, therefore, the center is $\left(0 , 0\right)$

Referring, again, to equation [1] the vertices are located at the points:

$\left(h , k - a\right) \mathmr{and} \left(h , k + a\right)$

In the given equation, $a = 3$, therefore, the vertices are located at the points:

$\left(0 , - 3\right) \mathmr{and} \left(0 , 3\right)$

Here is a graph of the hyperbola: