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 - 1)^2+(y - 2)^2=\frac{1}{49}) radius: center: () question help: video ebook written example message instructor submit question

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

Comparing $(x - 1)^2+(y - 2)^2=\frac{1}{49}$ with $(x - h)^2+(y - k)^2=r^2$, we have $h = 1$ and $k = 2$. So the center of the circle is $(1,2)$.

Step3: Calculate the radius

Since $r^2=\frac{1}{49}$, taking the square - root of both sides, we get $r=\sqrt{\frac{1}{49}}=\frac{1}{7}\approx0.143$.

Answer:

Radius: $\frac{1}{7}\approx0.143$
Center: $(1,2)$