Question

find the center and radius of the circle. write the standard form of the equation. the center of the circle is (5.5,3). (type an ordered pair.) the radius of the circle is

Explanation:

Step1: Recall circle - center and radius concept

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. Given the center $(h,k)=(5.5,3)$.

Step2: Calculate the radius using distance formula

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let the center of the circle be $(h,k)=(5.5,3)$ and a point on the circle be $(x,y)=(4,3)$. Then $r=\sqrt{(5.5 - 4)^2+(3 - 3)^2}=\sqrt{(1.5)^2+0^2}=1.5$.

Answer:

$1.5$