Question

Find the center and radius of the circle. Write the standard form of the equation.

Short answer

Center is $\left(1,2\right)$.

Radius is equal to $2$units.

Standard form of the equation is$(x-1{)}^2+(y-2{)}^2=4$.

Step-by-step solution

Step 1. Given information

Figure of a circle is as follows:

Step 2. Find the center and radius of a circle.

Radius is the distance between the center and any point on the circle

In this case, radius is the distance between the points $(1,2)$and $\left(1,0\right)$.

Radius$=\sqrt{(1-1{)}^2+(2-0{)}^2}$

$$\begin{gathered} =\sqrt{0+4} \\ =\sqrt{4} \\ =2 \end{gathered}$$

From the given graph, we can see that the center is$\left(1,2\right)$.

Step 3. Find the standard form of the equation.

Equation of a circle with center $\left(h,k\right)$and radius $r$is $(x-h{)}^2+(y-k{)}^2=r^2$.

Therefore, equation of the circle with center $\left(1,2\right)$and radius $2$is

$\begin{array}{rcl}(x-1{)}^2+(y-2{)}^2& =& 2^2\\ (x-1{)}^2+(y-2{)}^2& =& 4\end{array}$