Math Snap

STEP 1

What is this asking?
We need to find the equation of a circle drawn on a graph, and write it in the standard form $(x-h)^2 + (y-k)^2 = r^2$.
Watch out!
Don't mix up the coordinates of the center $(h, k)$ and the radius $r$!

STEP 2

1. Find the Center
2. Find the Radius
3. Write the Equation

STEP 3

Alright, let's locate the center of this awesome circle!
Looking closely at the graph, we can see that the center of the circle is at the point $(0, 6)$.
So, our center is $(h, k) = (0, 6)$.

STEP 4

Now, let's find the radius.
The radius is the distance from the center to any point on the circle.
We can easily see that the circle goes from $y=3$ to $y=9$, which means the diameter is $9-3=6$.
Since the radius is half of the diameter, our radius is $r = \frac{6}{2} = 3$.

STEP 5

Time to plug in our values into the standard form equation of a circle: $(x-h)^2 + (y-k)^2 = r^2$.

STEP 6

We found that the center is $(0, 6)$, so $h = 0$ and $k = 6$.
We also found that the radius is $3$, so $r = 3$.

STEP 7

Substituting these values into the equation, we get $(x-0)^2 + (y-6)^2 = 3^2$.

STEP 8

Simplifying, we get $x^2 + (y-6)^2 = 9$.
Boom!

The equation of the circle in standard form is $x^2 + (y-6)^2 = 9$.