Center and radius of (x - 1)^2 + (y - 4)^2 = 9

Step by step

The question

Question: find the center and the radius of (x − 1)² + (y − 4)² = 9.

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 like x − h.

So h = 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 = 9.

r times r is 9.

So r is the square root of 9.

3 times 3 is 9.

So r = 3.

So the center is (1, 4) and the radius is 3.

4 Check

Let's check: draw the circle.

Center (1, 4), radius 3.

Put the center on the grid.

Draw the circle around it.

Its right end is on the circle: (4, 4), 3 to the right of the center.

Put x = 4 and y = 4 in.

We get 3² + 0².

9 plus 0 is 9, 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.