Question

question 4 of 10
the equation of a circle centered at the origin is ( x^{2}+y^{2}=64 ). what is the
radius of the circle?
a. 8
b. 4
c. 32
d. 64

Explanation:

Step1: Recall the standard equation of a circle

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

Step2: Compare with the given equation

Given \(x^{2}+y^{2}=64\), we have \(r^{2} = 64\).

Step3: Solve for \(r\)

Take the square root of both sides: \(r=\sqrt{64}\). Since \(r>0\) (radius is a non - negative quantity), \(r = 8\).

Answer:

A. 8