Question

write the standard form of the equation of the circle with the given center and radius. center (0,0), r = 11 the equation for the circle in standard form is (simplify your answer)

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Substitute the given values

Here, \(h = 0\), \(k = 0\), and \(r = 11\). Substituting these into the formula gives \((x - 0)^2+(y - 0)^2=11^2\).

Step3: Simplify the equation

Simplifying \((x - 0)^2+(y - 0)^2=11^2\) results in \(x^2 + y^2=121\).

Answer:

\(x^2 + y^2=121\)