Step by step
The question
Question: find the center and the radius of (x − 2)² + (y + 3)² = 16.
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
x − 2 is like x − h.
So h = 2.
y + 3 is the same as y − (−3).
Taking away a negative is adding.
So k = −3.
Careful: the sign turns.
+ 3 in the bracket means the center has −3.
So the center is (2, −3).
3 Find the radius
r² is the number on the right: r² = 16.
r times r is 16.
So r is the square root of 16.
4 times 4 is 16.
So r = 4.
So the center is (2, −3) and the radius is 4.
4 Check
Let's check: draw the circle.
Center (2, −3), radius 4.
Put the center on the grid.
Draw the circle around it.
Its right end is on the circle: (6, −3), 4 to the right of the center.
Put x = 6 and y = −3 in.
We get 4² + 0².
16 plus 0 is 16, 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.