Question

write the standard form of the equation of the circle with the given center and radius. center (0,0), r = 3. the equation for the circle in standard form is (simplify your answer)

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 the given values

Given center \((h,k)=(0,0)\) and \(r = 3\). Substitute \(h = 0\), \(k = 0\), and \(r = 3\) into the formula: \((x-0)^2+(y - 0)^2=3^2\).

Step3: Simplify the equation

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

Answer:

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