Question

what is the radius for the circle given by the equation $x^{2}+(y - 1)^{2}=12$?
round your answer to the nearest thousandth. ________

Explanation:

Step1: Recall the standard circle equation

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.

Step2: Compare with the given equation

Given \(x^2+(y - 1)^2 = 12\), we have \(r^2=12\).

Step3: Solve for \(r\)

Take the square root of both sides: \(r=\sqrt{12}\). Simplify \(\sqrt{12}=2\sqrt{3}\approx2\times1.732 = 3.464\) (rounded to the nearest thousandth).

Answer:

\(3.464\)