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

The domain of the circle is represented by all the possible x values. Similarly, the range of the circle are all the possible y values. The formula of the circle is ##(x- a)^2 +(y-b) ^2 =r^2##, where r is the radius of the circle and the point with coordinates ##(a, b)## is the center of the circle. The domain of a circle is [a-r; a+r] The range of the circle is [b-r; b+r].

Let's take an example. The equation defining a circle is ##(x-2)^2+(y-4)^2-49=0##. We first rewrite it to standard form. The standard form of the circle is ##(x- a)^2 +(y-b) ^2 =r^2##, which in this case is ##(x- 2)^2 +(y-4) ^2 =7^2## The radius: ##r=7## The center: ##(2, 4)## We can now immediately find the domain and the range: The domain of ths circle is [2-7; 2+7], which equals to [-5;9]. The range of the circle is [4-7;4+7], which equals to [-3;11].

Here is the illustration: graph{(x-2)^2+(y-4)^2=7^2 [-10, 10, -5, 5]} All x values corresponding to points on the graph are the domain (from -5 to 9), and all y values that corresponding to points on the graph are the range (from -3 to 11).