# How do you write the equation of the circle in standard form, identify the center and radius of x^2+y^2-10x-6y+25=0?

Feb 22, 2017

This is the equation of a circle, center $= \left(5 , 3\right)$ and radius $r = 3$

#### Explanation:

We rewrite the equation by completing the squares

${x}^{2} + {y}^{2} - 10 x - 6 y + 25 = 0$

$\left({x}^{2} - 10 x\right) + \left({y}^{2} - 6 y\right) = - 25$

$\left({x}^{2} - 10 x + 25\right) + \left({y}^{2} - 6 y + 9\right) = - 25 + 25 + 9$

${\left(x - 5\right)}^{2} + {\left(y - 3\right)}^{2} = {3}^{2}$

This is the equation of a circle, center $= \left(5 , 3\right)$ and radius $r = 3$

graph{(x^2+y^2-10x-6y+25)((x-5)^2+(y-3)^2-0.003)=0 [-4.97, 12.81, -1.88, 7.01]}