# How do you find the domain and range of a circle?

Jul 13, 2018

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

where the centre is (a,b) and the radius is r

The graph is a circle so all the points are enclosed in it

The domain is the values for x so you subtract the radius from the centre coordinate and you add the radius to it

The range is the values for y so you do the same to the y coordinate

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

The centre is (-2,4) radius is 5

Domain $\implies - 2 - 5 = - 7$
and $- 2 + 5 = 3$
[-7,3]

Range $\implies 4 - 5 = - 1$
and $4 + 5 = 9$
[-1,9]