Step by step
The question
Question: find the center and the radius of (x − 1)² + (y − 2)² = −4.
(x − 1)2 + (y − 2)2 = −4
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 − 1 is like x − h.
So h = 1.
h = 1
x − 1 ↔ x − h
y − 2 is like y − k.
So k = 2.
k = 2
y − 2 ↔ y − k
So the center is (1, 2).
center = (1, 2)
3 Find the radius
r² would be −4.
But r² is r times r.
A square is never negative.
r2 = −4 impossible
So there is no circle.
This equation is impossible.
Let's look back.
First: compare with the rule.
Then: find the center.
Last: find the radius.
Answer
r2 = −4 impossible