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 units. the center of the circle is at ( , ).

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify the center

For the equation $(x - 5)^2+y^2 = 81$, comparing with the standard - form $(x - h)^2+(y - k)^2=r^2$, we have $h = 5$ and $k = 0$. So the center of the circle is $(5,0)$.

Step3: Identify the radius

Since $r^2=81$, taking the square - root of both sides, we get $r=\sqrt{81}=9$ (we take the positive value for the radius as it represents a distance).

Answer:

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