Step by step
The question
Question: find the center and the radius of (x + 2)² + (y − 3)² = 0.
(x + 2)2 + (y − 3)2 = 0
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 + 2 is the same as x − (−2).
Taking away a negative is adding.
x + 2 = x − (−2)
So h = −2.
h = −2
Careful: the sign turns.
+ 2 in the bracket means the center has −2.
+ 2 → h = −2
y − 3 is like y − k.
So k = 3.
k = 3
y − 3 ↔ y − k
So the center is (−2, 3).
center = (−2, 3)
3 Find the radius
r² is the number on the right: r² = 0.
r2 = 0
So r = 0.
A circle with radius 0 is impossible: it is just one point, the center (−2, 3).
r = 0
Let's look back.
First: compare with the rule.
Then: find the center.
Last: find the radius.
Answer
r = 0