# How do you determine the domain and range of the relation x^2 + y^2 = 1 and x^2 + y^2 = 100? i know it makes a circle but I'm just confused about the steps that you have to take in order to find the domain and range.  thankss in advance! You should notice that each given equation describes a circle centered at origin, with the radius r.

You need to remember the equation of the circle centered at origin such that:

`x^2 + y^2 = r^2`

Comparing the first equation, `x^2 + y^2 =1` , to the general equation of the circle,`x^2 + y^2 = r^2` , yields that `r^2 = 1 => r = 1` .

Since the circle is centered at origin, its diameter is of length 2, meaning that the domain and the range are the same, `[-1,1].`

Comparing the first equation, `x^2 + y^2 = 100` , to the general equation of the circle, `x^2 + y^2 = r^2`  , yields that`r^2 = 100 ` `=> r = 10` .

Since the circle is centered at origin, its diameter is of length 20, meaning that the domain and the range are the same, `[-10,10].`

Approved by eNotes Editorial Team For x^2+y^2=1, you already know the graph is a circle centered at (0,0) with radius 1. Think of squeezing the graph down onto the x axis. It'll overlap the axis when -1<=x<=1, or [-1,1] in interval notation, so that's the domain.

Do something similar for the range, except now compress the graph onto the y axis. It overlaps from -1<=y<=1, so that's the range.

The same idea applies to x^2+y^2=100. This is a circle centered at the origin with radius 10, so the domain and range will now both be [-10,10].

Approved by eNotes Editorial Team 