Question

write the equation of this circle in standard form.

Explanation:

Step1: Identify center and radius

The center of the circle is at the origin \((0,0)\) (since it's at the intersection of the x - and y - axes). To find the radius, we can see that the circle extends from \(x=-6\) to \(x = 6\) (or \(y=-6\) to \(y = 6\)), so the radius \(r = 6\).

Step2: Use 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. Here, \(h = 0\), \(k = 0\), and \(r = 6\). Substituting these values in, we get \((x - 0)^2+(y - 0)^2=6^2\), which simplifies to \(x^{2}+y^{2}=36\).

Answer:

\(x^{2}+y^{2}=36\)