Question

write the equation of this circle in standard form.

Explanation:

Step1: Recall circle standard form

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Step2: Identify the center

From the graph, the center of the circle is at \((0, 1)\) (since it's on the y - axis, \(x = 0\), and \(y = 1\) as seen from the grid).

Step3: Determine the radius

The radius is the distance from the center to the edge. Looking at the graph, the distance from the center \((0,1)\) to the rightmost point (or any point on the circle) is 4 units (from \(x = 0\) to \(x = 4\) on the x - axis, or from \(y = 1\) to \(y = 5\) on the y - axis, etc.). So \(r = 4\).

Step4: Substitute into the standard form

Substitute \(h = 0\), \(k = 1\), and \(r = 4\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x - 0)^2+(y - 1)^2 = 4^2\), which simplifies to \(x^2+(y - 1)^2 = 16\).

Answer:

\(x^2+(y - 1)^2 = 16\)