Question

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 - 4)^2+(y - 3)^2 = 25 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 $(x - 4)^2+(y - 3)^2=25$, we have $h = 4$, $k = 3$ and $r^2=25$, so $r = 5$.

Step2: Find the domain

The $x$ - values of a circle centered at $(h,k)$ with radius $r$ range from $h - r$ to $h + r$. Here, $h = 4$ and $r = 5$. So the minimum $x$ - value is $4-5=-1$ and the maximum $x$ - value is $4 + 5=9$.

Answer:

$[-1,9]$