Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the domain and range.
(x + 5)^2+(y - 6)^2 = 36
the center is
(type an ordered pair. simplify your answer.)

Explanation:

Step1: Recall circle - equation form

The standard form of a circle's equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius.

Step2: Identify the center

For the equation $(x + 5)^2+(y - 6)^2 = 36$, we can rewrite it as $(x-(-5))^2+(y - 6)^2=6^2$. So, $h=-5$ and $k = 6$. The center is $(-5,6)$.

Step3: Identify the radius

Since $r^2=36$, then $r = 6$ (we take the positive square - root because radius is non - negative).

Step4: Find the domain

The left - most point of the circle is $x=-5 - 6=-11$ and the right - most point is $x=-5 + 6 = 1$. So the domain is $[-11,1]$.

Step5: Find the range

The bottom - most point of the circle is $y=6 - 6 = 0$ and the top - most point is $y=6+6 = 12$. So the range is $[0,12]$.

Answer:

Center: $(-5,6)$
Radius: $6$
Domain: $[-11,1]$
Range: $[0,12]$