Question

write the standard equation of ⊙p shown to the right. the standard form of the equation of the circle is (type an equation. simplify your answer.)

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius.

Step2: Identify the center of the circle

From the graph, the center of the circle $P$ is at $(2,6)$. So $h = 2$ and $k = 6$.

Step3: Determine the radius of the circle

By counting the grid - squares, the radius $r = 2$.

Step4: Substitute values into the formula

Substitute $h = 2$, $k = 6$, and $r = 2$ into the standard - form equation: $(x - 2)^2+(y - 6)^2=2^2$.

Step5: Simplify the equation

$(x - 2)^2+(y - 6)^2 = 4$.

Answer:

$(x - 2)^2+(y - 6)^2=4$