Question

what is the equation of the circle? enter an answer in each box to complete the equation. be sure to include a plus or minus symbol where needed. (x )^2+(y )^2=

Explanation:

Step1: Identify the center of the circle

From the graph, assume the center of the circle is \((h,k)\). By visual - inspection, if we assume the center is at \((3,9)\) (counting the grid - squares).

Step2: Determine the radius of the circle

The radius \(r\) is the distance from the center \((3,9)\) to the point \((x,y)\) on the circle. Using the right - triangle formed (with the dashed lines), by counting the grid - squares, the vertical distance is \(4\) and the horizontal distance is \(3\). Using the Pythagorean theorem \(r=\sqrt{3^{2}+4^{2}} = 5\).

Step3: Write the equation of the circle

The standard form of the equation of a circle is \((x - h)^{2}+(y - k)^{2}=r^{2}\). Substituting \(h = 3\), \(k = 9\), and \(r = 5\) into the equation, we get \((x - 3)^{2}+(y - 9)^{2}=25\).

Answer:

\((x - 3)^{2}+(y - 9)^{2}=25\)