# How do you graph x^2+y^2-2x-4y-4=0?

Jul 17, 2018

#### Explanation:

The equation is

${x}^{2} + {y}^{2} - 2 x - 4 y - 4 = 0$

Complete the square

${x}^{2} - 2 x + {y}^{2} - 4 y = 4$

${x}^{2} - 2 x + 1 + {y}^{2} - 4 y + 4 = 4 + 1 + 4$

Factorise

${\left(x - 1\right)}^{2} + {\left(y - 2\right)}^{2} = 9 = {3}^{2}$

This is the equation of a circle, center $C = \left(1 , 2\right)$ and radius $r = 3$

The graph is shown below

graph{(x^2+y^2-2x-4y-4)=0 [-8.065, 7.735, -2.18, 5.72]}