Question

a circle has a diameter of 12 units, and its center lies on the x - axis. what could be the equation of the circle? check all that apply.
(x - 12)^2 + y^2 = 12
(x - 6)^2 + y^2 = 36
x^2 + y^2 = 12
x^2 + y^2 = 144
(x + 6)^2 + y^2 = 36
(x + 12)^2 + y^2 = 144

Explanation:

Step1: Find the radius

The diameter $d = 12$, so the radius $r=\frac{d}{2}=\frac{12}{2}=6$.

Step2: Recall the equation of a circle

The standard - form equation of a circle with center $(h,k)$ and radius $r$ is $(x - h)^2+(y - k)^2=r^2$. Since the center lies on the $x$ - axis, $k = 0$. The equation becomes $(x - h)^2+y^2=r^2$. Substituting $r = 6$, we get $(x - h)^2+y^2 = 36$, where $h$ can be any real number. When $h = 6$, the equation is $(x - 6)^2+y^2 = 36$; when $h=-6$, the equation is $(x + 6)^2+y^2 = 36$.

Answer:

B. $(x - 6)^2+y^2 = 36$, E. $(x + 6)^2+y^2 = 36$