# How do you write an equation for a circle with center (2,4) and passes through point (5, 9)?

Apr 16, 2016

${\left(x - 2\right)}^{2} + {\left(y - 4\right)}^{2} = 34$

#### Explanation:

The radius can be found using Pythagoras Theorem

$r = \sqrt{{\left(5 - 2\right)}^{2} + {\left(9 - 4\right)}^{2}} = \sqrt{34}$

For a circle with radius $r$ and centered at $\left(a , b\right)$, its cartesian equation is

${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

Therefore. for a circle with radius $\sqrt{34}$ and centered at $\left(2 , 4\right)$. its cartesian equation is

${\left(x - 2\right)}^{2} + {\left(y - 4\right)}^{2} = 34$