Step by step
The question
Question: find the center and the radius of x² + (y − 5)² = 20.
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 = 20.
r times r is 20.
So r is the square root of 20.
20 is not a square number.
So we keep √20.
That is the exact answer.
With a calculator, √20 is about 4.5, to the nearest tenth.
So the center is (0, 5) and the radius is √20.
4 Check
Let's check: draw the circle.
Center (0, 5), radius about 4.5.
Put the center on the grid.
Draw the circle around it.
This point is on the circle: (2, 9).
It is 2 across and 4 up from the center.
Put x = 2 and y = 9 in.
We get 2² + 4².
4 plus 16 is 20, 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.