Let’s solve this step by step.
We are given the equation of a circle:
(x – 3)² + (y + 2)² = 4
Step 1: Recall the standard form of a circle
The standard form is:
(x – h)² + (y – k)² = r²
where:
-
(h, k) is the center of the circle
-
r is the radius
Step 2: Rewrite the given equation to match the standard form
Our equation:
(x – 3)² + (y + 2)² = 4
Notice that
(y + 2) can be written as
(y – (–2)), so we rewrite it:
→
(x – 3)² + (y – (–2))² = 2²
Now it matches the standard form!
Step 3: Identify h, k, and r
From
(x – 3)² + (y – (–2))² = 2²:
- h = 3
- k = –2
- r = 2 (since 2² = 4)
So, the
center is at
(3, –2) and the
radius is
2.
Step 4: Graph the circle
To graph it:
1. Plot the center point at
(3, –2) on the coordinate plane.
2. From that point, go 2 units up, down, left, and right — because the radius is 2.
- Up: (3, –2 + 2) = (3, 0)
- Down: (3, –2 – 2) = (3, –4)
- Left: (3 – 2, –2) = (1, –2)
- Right: (3 + 2, –2) = (5, –2)
3. Draw a smooth circle through those points.
That’s your graph!
---
Final Answer:
Center: (3, –2), Radius: 2
Parent Tip: Review the logic above to help your child master the concept of circles in the coordinate plane worksheet answers.
