Question

use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form. a. type the equation in center-radius form. (simplify your answer.)

Explanation:

Step1: Determine the center of the circle

The center of the circle is \((h,k)=(6,3)\) (from the given points on the graph).

Step2: Calculate the radius

Using the distance formula between the center \((6,3)\) and a point on the circle (say \((6,5)\)), \(r = 2\) (since the vertical distance from \((6,3)\) to \((6,5)\) is \(|5 - 3|=2\)).

Step3: Write the center - radius form

The center - radius form of a circle is \((x - h)^2+(y - k)^2=r^2\). Substituting \(h = 6\), \(k = 3\), and \(r = 2\), we get \((x - 6)^2+(y - 3)^2=4\).

Answer:

\((x - 6)^2+(y - 3)^2=4\)