Step by step
The question
Question: find the center and the radius of x² + (y − 5)² = 9.
1 Compare with the rule
Every circle has this form: (x − h)² + (y − k)² = r².
The center is (h, k).
The radius is r.
2 Find the center
x² is the same as (x − 0)²: taking away 0 changes nothing.
So h = 0.
y − 5 is like y − k.
So k = 5.
So the center is (0, 5).
3 Find the radius
r² is the number on the right: r² = 9.
r times r is 9.
So r is the square root of 9.
3 times 3 is 9.
So r = 3.
So the center is (0, 5) and the radius is 3.
4 Check
Let's check: draw the circle.
Center (0, 5), radius 3.
Put the center on the grid.
Draw the circle around it.
Its right end is on the circle: (3, 5), 3 to the right of the center.
Put x = 3 and y = 5 in.
We get 3² + 0².
9 plus 0 is 9, the number on the right.
Right!
Let's look back.
First: compare with the rule.
Then: find the center.
Then: find the radius.
Last: check.