Question

this circle is centered at the origin, and the length of its radius is 2. what is the circles equation?
a. $x^{2}+y = 2$
b. $x^{2}+y^{2}=4$
c. $x^{4}+y^{4}=4$
d. $x^{2}+y^{2}=2$

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: Substitute the value of the radius

Given \(r = 2\), then \(r^{2}=2^{2}=4\).

Step3: Write the equation of the circle

Substituting \(r^{2}=4\) into the standard equation \(x^{2}+y^{2}=r^{2}\), we get \(x^{2}+y^{2}=4\).

Answer:

B. \(x^{2}+y^{2}=4\)