Question

find the center and radius of the circle with the given equation. x^2+(y - 1)^2=16 center (x,y)=( ) radius sketch the circle.

Explanation:

Step1: Recall circle - equation form

The standard form of the equation of a circle 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 given equation $x^{2}+(y - 1)^{2}=16$, comparing with the standard form $(x - h)^2+(y - k)^2=r^2$, we have $h = 0$ and $k = 1$. So the center $(x,y)=(0,1)$.

Step3: Identify the radius

Since $r^{2}=16$, taking the square - root of both sides (and considering $r>0$), we get $r = 4$.

Answer:

center $(x,y)=(0,1)$
radius $4$