Step by step
The question
Question: find the center and the radius of (x + 1)² + (y − 4)² = 36.
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 + 1 is the same as x − (−1).
Taking away a negative is adding.
So h = −1.
Careful: the sign turns.
+ 1 in the bracket means the center has −1.
y − 4 is like y − k.
So k = 4.
So the center is (−1, 4).
3 Find the radius
r² is the number on the right: r² = 36.
r times r is 36.
So r is the square root of 36.
6 times 6 is 36.
So r = 6.
So the center is (−1, 4) and the radius is 6.
4 Check
Let's check: draw the circle.
Center (−1, 4), radius 6.
Put the center on the grid.
Draw the circle around it.
Its right end is on the circle: (5, 4), 6 to the right of the center.
Put x = 5 and y = 4 in.
We get 6² + 0².
36 plus 0 is 36, 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.