Question

question 15, 2.8. part 4 of 5 give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the relations domain and range. $x^{2}+y^{2}=81$ what is the center of the circle? the circle is centered at the point (0,0). (type an ordered pair.) what is the radius of the circle? the radius of the circle is 9. (type an integer or a fraction.) use the graphing tool to graph the circle. what is the domain of the relation? the domain is . (type your answer in interval notation.)

Explanation:

Step1: Recall circle - equation form

The standard form of a circle equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius. For the equation $x^{2}+y^{2}=81$, we can rewrite it as $(x - 0)^2+(y - 0)^2 = 9^2$.

Step2: Determine domain

The domain of a circle centered at the origin with radius $r$ is given by the $x$ - values of the points on the circle. The left - most and right - most points of the circle $x^{2}+y^{2}=r^{2}$ occur when $y = 0$. Solving $x^{2}=r^{2}$ gives $x=\pm r$. Here $r = 9$, so the domain is $[-9,9]$.

Answer:

$[-9,9]$