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: Find the center of the circle

The center of the circle is given by the point \((h,k)=(4,3)\) (from the point \((4,3)\) in the graph).

Step2: Calculate the radius

The radius \(r\) is the distance from the center \((4,3)\) to a point on the circle, say \((3,3)\). Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), we have \(r=\sqrt{(4 - 3)^2+(3 - 3)^2}=\sqrt{1+0}=1\)

Step3: Write the center - radius form

The center - radius form of a circle is \((x - h)^2+(y - k)^2=r^2\). Substituting \(h = 4\), \(k = 3\) and \(r = 1\), we get \((x - 4)^2+(y - 3)^2=1\)

Answer:

\((x - 4)^2+(y - 3)^2=1\)