# How do you find the center and radius of the circle given (x-3)^2+(y+7)^2=50?

Dec 4, 2016

The center is $\left(3 , - 7\right)$ and the radius is $5 \sqrt{2}$.

#### Explanation:

Find the center and radius of ${\left(x - 3\right)}^{2} + {\left(y + 7\right)}^{2} = 50$

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

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

$\implies \left(h , k\right) = \left(3 , - 7\right)$ (note that the signs are opposite of the signs inside the parentheses)

${r}^{2} = 50$

To find r, square root both sides

$\sqrt{{r}^{2}} = \sqrt{50}$

$r = \sqrt{25 \cdot 2}$

$r = 5 \sqrt{2}$