Question

question 31 of 52 what is the radius for a circle whose equation is $x^2 + y^2 = 64$? a. 16 b. 8 c. 32 d. 64

Explanation:

Step1: Recall circle equation

The standard equation of a circle is \((x - h)^2 + (y - k)^2 = r^2\), where \((h,k)\) is the center and \(r\) is the radius. For the equation \(x^2 + y^2 = 64\), we can rewrite it as \((x - 0)^2 + (y - 0)^2 = 8^2\) (since \(64 = 8^2\)).

Step2: Identify radius

By comparing with the standard form, we see that \(r^2 = 64\), so taking the square root of both sides (and since radius is positive), we get \(r = \sqrt{64} = 8\)? Wait, no, wait. Wait, \(x^2 + y^2 = 64\) is \(r^2 = 64\), so \(r=\sqrt{64}=8\)? Wait, no, wait, 8 squared is 64? Wait, 88=64, yes. Wait, but the options: A is 16, B is 8, C is 32, D is 64. Wait, no, wait, the equation is \(x^2 + y^2 = 64\), so \(r^2 = 64\), so \(r = 8\)? Wait, no, 8 squared is 64, so radius is 8? But wait, no, wait, 88=64, so the radius is 8? But let's check again. The standard form is \(x^2 + y^2 = r^2\), so if \(r^2 = 64\), then \(r = \sqrt{64} = 8\). So the radius is 8, which is option B. Wait, but wait, maybe I made a mistake. Wait, 8 squared is 64, so yes, radius is 8.

Wait, no, wait, the equation is \(x^2 + y^2 = 64\), so \(r^2 = 64\), so \(r = 8\). So the answer is B.

Answer:

B. 8