Question

use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.
question 3, 2.2.23
part 1 of 2
hw score: 91.3%, 13.5 of 14 points
points: 0.5 of

a. type the equa in center-radius form.
(simplify your answer.)

Explanation:

Step1: Find the center of the circle

The center of the circle is the mid - point between \((0,2)\) and \((10,2)\). Using the mid - point formula \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\), we have \((\frac{0 + 10}{2},\frac{2+2}{2})=(5,2)\)

Step2: Calculate the radius

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) between the center \((5,2)\) and the point \((0,2)\).

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Step3: Write the equation in center - radius form

The center - radius form of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius. Substituting \(h = 5,k = 2,r = 5\) into the formula, we get \((x - 5)^2+(y - 2)^2=25\)

Answer:

\((x - 5)^2+(y - 2)^2=25\)