Question

practice working with equations of circ
the equation of a circle is $x^{2}+(y - 10)^{2}=16$.
the radius of the circle is units.
the center of the circle is at .

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify the radius

Given the equation $x^{2}+(y - 10)^{2}=16$, we can rewrite it as $(x - 0)^2+(y - 10)^{2}=4^{2}$. Comparing with the standard - form, we have $r^{2}=16$, so $r = 4$.

Step3: Identify the center

Comparing $(x - 0)^2+(y - 10)^{2}=4^{2}$ with $(x - a)^2+(y - b)^2=r^2$, we get $a = 0$ and $b = 10$. So the center is $(0,10)$.

Answer:

The radius of the circle is 4 units.
The center of the circle is at $(0,10)$.