Question

if the equation of a circle is $x^{2}+y^{2}=144$, what is the radius of the circle?
a. 144
b. 72
c. 36
d. 12

Explanation:

Step1: Recall the standard 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 given equation \(x^{2}+y^{2}=144\), it can be written as \((x - 0)^2+(y - 0)^2=r^{2}\), so \(r^{2}=144\).

Step2: Solve for \(r\)

Take the square root of both sides: \(r=\sqrt{144}\). Since radius is non - negative, \(r = 12\).

Answer:

d. 12