Question

write the standard form of the equation of the circle with the graph shown to the right.
what is the standard form of the equation of the circle to the right?
(simplify your answers.)

Explanation:

Step1: Identify the center of the circle

From the graph, the center of the circle \((h,k)\) is at \((3,0)\) (by looking at the coordinates of the center point on the grid).

Step2: Determine the radius of the circle

By counting the grid units from the center to the edge of the circle, we can see that the radius \(r = 5\) (for example, from \(x = 3\) to \(x = 8\) is 5 units, or from \(y = 0\) to \(y = 5\) or \(y=- 5\) is 5 units).

Step3: Use the standard form of the circle's equation

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\). Substituting \(h = 3\), \(k = 0\), and \(r = 5\) into the formula, we get \((x - 3)^2+(y - 0)^2=5^2\), which simplifies to \((x - 3)^2+y^2 = 25\).

Answer:

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