Step by step
The question
Question: find the center and the radius of (x + 5)² + (y + 2)² = 1.
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 + 5 is the same as x − (−5).
Taking away a negative is adding.
So h = −5.
Careful: the sign turns.
+ 5 in the bracket means the center has −5.
y + 2 is the same as y − (−2).
Taking away a negative is adding.
So k = −2.
So the center is (−5, −2).
3 Find the radius
r² is the number on the right: r² = 1.
r times r is 1.
So r is the square root of 1.
1 times 1 is 1.
So r = 1.
So the center is (−5, −2) and the radius is 1.
4 Check
Let's check: draw the circle.
Center (−5, −2), radius 1.
Put the center on the grid.
Draw the circle around it.
Its right end is on the circle: (−4, −2), 1 to the right of the center.
Put x = −4 and y = −2 in.
We get 1² + 0².
1 plus 0 is 1, 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.