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
the circle is centered at the point (4,3).
(type an ordered pair.)
what is the radius of the circle?
the radius of the circle is 5.
(type an integer or a fraction.)
use the graphing tool to graph the circle.
what is the domain of the relation?
the domain is -1,9
(type your answer in interval notation.)
what is the range of the relation?
the range is
(type your answer in interval notation.)

Explanation:

Step1: Recall circle - domain and range relationship

The domain and range of a circle centered at $(h,k)$ with radius $r$ are found by considering the left - most, right - most, bottom - most, and top - most points. The $x$ - values of the circle are in the interval $[h - r,h + r]$ and the $y$ - values are in the interval $[k - r,k + r]$.

Step2: Identify values of $h$, $k$, and $r$

The equation of the circle is $(x - 4)^2+(y - 3)^2 = 25$, so $h = 4$, $k = 3$, and $r = 5$.

Step3: Calculate the range

For the $y$ - values (range), we use the formula $[k - r,k + r]$. Substitute $k = 3$ and $r = 5$ into the formula. We get $3-5=-2$ and $3 + 5=8$. So the range is $[-2,8]$.

Answer:

$[-2,8]$