Question

for the given equation, find each coordinate of the center exactly. also, find radius of the circle either exactly or rounded off to 3 decimal places. ((x + 2)^{2}+(y - 1)^{2}=\frac{1}{144}) radius: center: () question help: video ebook written example

Explanation:

Step1: Recall circle - equation form

The standard form of a circle 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 coordinates

For the equation $(x + 2)^2+(y - 1)^2=\frac{1}{144}$, we have $x+2=x - (- 2)$ and $y - 1$ as is. So, $h=-2$ and $k = 1$. The center of the circle is $(-2,1)$.

Step3: Calculate the radius

Since $r^2=\frac{1}{144}$, then $r=\sqrt{\frac{1}{144}}=\frac{1}{12}\approx0.083$.

Answer:

Radius: $\frac{1}{12}\approx0.083$
Center: $(-2,1)$