Question

write the equation of this circle in standard form.

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Determine the center of the circle

From the graph, the center of the circle is at the point \((0, 7)\) (since it lies on the y - axis, \(x = 0\), and the y - coordinate is 7, as it is halfway between 6 and 8 or can be seen from the grid).

Step3: Determine the radius of the circle

Looking at the graph, the distance from the center \((0,7)\) to the edge of the circle is 1 unit (since the circle spans from \(y = 6\) to \(y = 8\), so the radius \(r=1\)).

Step4: Substitute \(h\), \(k\), and \(r\) into the standard form equation

Substitute \(h = 0\), \(k = 7\), and \(r = 1\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x - 0)^2+(y - 7)^2=1^2\), which simplifies to \(x^2+(y - 7)^2 = 1\).

Answer:

\(x^2+(y - 7)^2 = 1\)