Question

what is the radius of the circle x^2 + y^2 = 121? write your answer in simplified, rationalized form.

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle centered at the origin \((0,0)\) is \(x^{2}+y^{2}=r^{2}\), where \(r\) is the radius.

Step2: Compare given equation with standard form

Given \(x^{2}+y^{2}=121\), and since \(x^{2}+y^{2}=r^{2}\), we have \(r^{2}=121\).

Step3: Solve for \(r\)

Taking the square - root of both sides, \(r = \sqrt{121}\). Since \(r>0\) (radius is a non - negative quantity), \(r = 11\).

Answer:

11