Question

what is the diameter of the circle $x^2 + y^2 = 36$? write your answer in simplified, rationalized form.

Explanation:

Step1: Recall circle equation form

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h,k)\) is the center and \(r\) is the radius. For the equation \(x^2 + y^2 = 36\), we can rewrite it as \((x - 0)^2 + (y - 0)^2 = 6^2\) (since \(36 = 6^2\)).

Step2: Determine the radius

From the equation, the radius \(r\) is \(6\) (because \(r^2 = 36\), so \(r=\sqrt{36}=6\)).

Step3: Calculate the diameter

The diameter \(d\) of a circle is related to the radius by the formula \(d = 2r\). Substituting \(r = 6\) into this formula, we get \(d = 2\times6 = 12\).

Answer:

12