Question

identify the radius and the center of a circle whose equation is $(x-5)^2 + y^2 = 81$.
the radius of the circle is $\boldsymbol{square}$ units.
the center of the circle is at $(\boldsymbol{square}, \boldsymbol{square}).$

Explanation:

Step1: Recall circle standard form

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

Step2: Match given equation to standard form

Given equation: $(x-5)^2+y^2=81$, which can be rewritten as $(x-5)^2+(y-0)^2=9^2$.

Step3: Identify center coordinates

Compare to standard form: $h=5$, $k=0$.

Step4: Identify radius value

Compare to standard form: $r=9$.

Answer:

The radius of the circle is 9 units.
The center of the circle is at (5, 0).