Question

write the standard form of the equation of the circle having the given radius and center. then, graph the circle. r = 3, center: (0,0) equation:

Explanation:

Step1: Recall circle - equation formula

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

Step2: Substitute given values

Given \(h = 0\), \(k = 0\), and \(r = 3\), we substitute into the formula: \((x-0)^2+(y - 0)^2=3^2\), which simplifies to \(x^{2}+y^{2}=9\).

Answer:

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