# How do you find the center and radius of the circle x^2 + y^2 - 8y = 9?

Mar 18, 2018

$\text{centre "(0,4), " radius } = 5$

#### Explanation:

we complete the square

${x}^{2} + {y}^{2} - 8 y = 9$

$\rightarrow {x}^{2} + \left({y}^{2} - 8 y + {4}^{2}\right) - {4}^{2} = 9$

${x}^{2} + {\left(y - 4\right)}^{2} - 16 = 9$

${x}^{2} + {\left(y - 4\right)}^{4} = 25$

cmp with the standard eqn

"centre "(a,b)," radius "=r

(x-a)^2+(y-b)^"=r^2#

we have

$\text{centre "(0,4), " radius } = 5$