Question

find the equation of a circle satisfying the given conditions. center (0,0), radius 12 the equation of the circle in standard form is . (type an 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 the given values

Given \(h = 0\), \(k = 0\), and \(r = 12\). Substitute these into the formula: \((x-0)^2+(y - 0)^2=12^2\).

Step3: Simplify the equation

\(x^{2}+y^{2}=144\).

Answer:

\(x^{2}+y^{2}=144\)