Question

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

Explanation:

Step1: Recall circle - center formula

The center of a circle is the mid - point of the diameter. If the endpoints of a diameter are \((x_1,y_1)\) and \((x_2,y_2)\), the mid - point formula is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Here, \(x_1=4,y_1 = 3,x_2=7,y_2 = 3\).

Step2: Calculate the x - coordinate of the center

\(x=\frac{4 + 7}{2}=\frac{11}{2}=5.5\)

Step3: Calculate the y - coordinate of the center

\(y=\frac{3+3}{2}=3\)

Answer:

\((5.5,3)\)