# How do you graph (x + 5)^2 + (y - 2)^2 = 49?

Jan 19, 2016

This is the general equation of a circle centred at $\left(- 5 , 2\right)$ and having radius $7$.

#### Explanation:

Any circle centred at $\left(a , b\right)$ and with radius $r$ has general equation ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$.

Therefore this is the general equation of a circle centred at $\left(- 5 , 2\right)$ and having radius $7$.

The graph will be the union of the following 2 semi-circles :

graph{2+sqrt((49-(x+5)^2) [-20.27, 20.27, -10.14, 10.12]}

graph{2-sqrt((49-(x+5)^2) [-20.27, 20.27, -10.14, 10.12]}

and it should look like this

graph{x^2 +10x + y^2 - 4y - 20 = 0 [-20.27, 20.27, -10.14, 10.12]}