Question

1. determine an equation for each circle. a)

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify center and radius

From the graph, the center of the circle is at the origin \((h = 0,k = 0)\) and the radius \(r = 3\).

Step3: Substitute values into formula

Substitute \(h = 0,k = 0,r = 3\) into the equation \((x - h)^2+(y - k)^2=r^2\), we get \((x-0)^2+(y - 0)^2=3^2\).

Answer:

\(x^{2}+y^{2}=9\)