Center and radius of (x - 3)^2 + (y - 2)^2 = 25 Step by Step

Step by step

The question

Question: find the center and the radius of (x − 3)² + (y − 2)² = 25.

(x − 3)² + (y − 2)² = 25

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.

(x − h)² + (y − k)² = r²

2 Find the center

x − 3 is like x − h.

So h = 3.

h = 3

x − 3 ↔ x − h

y − 2 is like y − k.

So k = 2.

k = 2

y − 2 ↔ y − k

So the center is (3, 2).

center = (3, 2)

3 Find the radius

r² is the number on the right: r² = 25.

r² = 25

r times r is 25.

So r is the square root of 25.

r = √25

5 times 5 is 25.

5 × 5 = 25

So r = 5.

r = 5

So the center is (3, 2) and the radius is 5.

center (3, 2) and r = 5

4 Check

Let's check: draw the circle.

Center (3, 2), radius 5.

Put the center on the grid.

Draw the circle around it.

Its right end is on the circle: (8, 2), 5 to the right of the center.

Put x = 8 and y = 2 in.

We get 5² + 0².

(8 − 3)² + (2 − 2)² = 5² + 0²

25 plus 0 is 25, the number on the right.

Right!

= 25 + 0 = 25

Let's look back.

First: compare with the rule.

Then: find the center.

Then: find the radius.

Last: check.

Answer