Answer: Center = (1, 5)
Radius = 5
Step-by-step explanation:
The standard form for a circle is: (x - h)² + (y - k)² = r² where
- Center = (h, k)
- Radius = r
First, group the x's and group the y's in order to complete the square.
x² - 2x + y² - 10y = -1
↓ ↓
(-2/2)²=1 (-10/2)²=25
Add those values to BOTH sides:
x² - 2x + 1 + y² - 10y + 25 = -1 + 1 + 25
Rewrite the left side as perfect squares and simplify the right side.
(x - 1)² + (y - 5)² = 25
We end up with (h, k) = (1, 5) this is the center
and r² = 25 --> r = 5 this is the radius
To graph the circle, place an x at the center (1, 5). Plot a point 5 units (the radius) to the right of the center, another point 5 units up from the center, a third point 5 units left from the center, and a fourth point 5 units down from the center. "Connect the dots" to create a circle.
