Question

write the equation of this circle in standard form.

Explanation:

Step1: Identify the center

The circle is centered at the origin \((0,0)\) since it's symmetric about both axes and the center is at the intersection of the axes.

Step2: Determine the radius

From the graph, the circle extends from \(x = -9\) to \(x = 9\) (or \(y=-9\) to \(y = 9\)), so the radius \(r = 9\).

Step3: Use the standard circle equation

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. Substituting \(h = 0\), \(k = 0\), and \(r = 9\), we get \((x - 0)^2+(y - 0)^2=9^2\), which simplifies to \(x^2 + y^2=81\).

Answer:

\(x^2 + y^2 = 81\)