Question

question 27 of 52 the circle below is centered at the origin and has a radius of 4. what is its equation? click here for long description a. ( x^2 - y^2 = 4 ) b. ( x^2 + y^2 = 4 ) c. ( x^2 - y^2 = 16 ) d. ( x^2 + y^2 = 16 )

Explanation:

Step1: Recall circle equation formula

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

Step2: Identify radius from problem

The circle has a radius \(r = 4\).

Step3: Substitute radius into formula

Substitute \(r = 4\) into the formula \(x^{2}+y^{2}=r^{2}\), we get \(x^{2}+y^{2}=4^{2}=16\).

Answer:

D. \(x^{2}+y^{2}=16\)