Step by step
The question
Question: find the center and the radius of (x + 2)² + y² = 49.
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 the same as x − (−2).
Taking away a negative is adding.
So h = −2.
Careful: the sign turns.
+ 2 in the bracket means the center has −2.
y² is the same as (y − 0)²: taking away 0 changes nothing.
So k = 0.
So the center is (−2, 0).
3 Find the radius
r² is the number on the right: r² = 49.
r times r is 49.
So r is the square root of 49.
7 times 7 is 49.
So r = 7.
So the center is (−2, 0) and the radius is 7.
4 Check
Let's check: draw the circle.
Center (−2, 0), radius 7.
Put the center on the grid.
Draw the circle around it.
Its right end is on the circle: (5, 0), 7 to the right of the center.
Put x = 5 and y = 0 in.
We get 7² + 0².
49 plus 0 is 49, 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.