Question

what is the equation of a circle centered at the origin with radius 13?
a. $x^{3}+y^{3}=13$
b. $x^{2}+y^{2}=169$
c. $x^{3}+y^{3}=169$
d. $x^{2}+y^{2}=13$

Explanation:

Step1: Recall circle - equation formula

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

Step2: Substitute the radius value

Given \(r = 13\), then \(r^{2}=13^{2}=169\). So the equation of the circle is \(x^{2}+y^{2}=169\).

Answer:

B. \(x^{2}+y^{2}=169\)