# How do you find the center, vertices, foci and asymptotes of x^2-y^2=100?

Jan 15, 2016

It can be recognized as the equation for a circle as it follows the general form ${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

#### Explanation:

This equation ${x}^{2} + {y}^{2} = 100$ can be rewritten as
${\left(x - 0\right)}^{2} + {\left(y - 0\right)}^{2} = {10}^{2}$

It can be recognized as the equation for a circle as it follows the general form ${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$ where $\left(h , k\right)$ is the center and $r$ is the radius.

Therefore it does not have vertices, foci or asymptotes.

The center is $\left(0 , 0\right)$ and the radius is $10$