Question

which is the equation of the circle shown below?
$(x-3)^2 + y^2 = 9$
$(x-3)^2 + y^2 = 3$
$(x+3)^2 + y^2 = 3$
$(x+3)^2 + y^2 = 9$

Explanation:

Step1: Identify circle center

From the graph, the center of the circle is at $(-3, 0)$.

Step2: Recall circle equation formula

The standard form of a circle's equation is $(x-h)^2 + (y-k)^2 = r^2$, where $(h,k)$ is the center and $r$ is the radius. Substitute $h=-3$, $k=0$:
$(x - (-3))^2 + (y - 0)^2 = r^2$
Simplify to: $(x+3)^2 + y^2 = r^2$

Step3: Calculate the radius

Count the grid units from the center $(-3,0)$ to any point on the circle (e.g., $(-3,3)$ or $(0,0)$). The radius $r=3$, so $r^2 = 3^2 = 9$.

Step4: Finalize the equation

Substitute $r^2=9$ into the equation: $(x+3)^2 + y^2 = 9$

Answer:

(x+3)^2 + y^2 = 9 (Option D)