# How do you find the center and radius of the circle given (x-4)^2+(y-1)^2=9?

Oct 15, 2016

The center is $\left(4 , 1\right)$ and the radius is $3$.

#### Explanation:

The general form of the circle equation is ${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

where $\left(h , k\right)$ is the center and $r$ is the radius.

In our example, ${\left(x - 4\right)}^{2} + {\left(y - 1\right)}^{2} = 9$

${r}^{2} = 9$ and $r = 3$

$\left(h , k\right) = \left(4 , 1\right)$

Note that because of the minus signs in the parentheses, you have to change the signs to find $h$ and $k$.

There is a somewhat silly saying in math that the "inside lies". In other words, the numbers in the parentheses are the opposite sign of the number you are trying to find.

In our example, even though the number inside the first set of parentheses is $- 4$, it is a "liar" and the answer is $+ 4$.