Question

Find the center (h,k) and radius r of the circle. Graph the equation. x^2 + y^2 - 2x - 10y + 1 = 0

Answer 1

Answer: Center = (1, 5)

Radius = 5

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.

Answer 2

Center: (1, 5)

Radius: r = 5

Explanation:

Step 1: Rewrite equation

x² - 2x + y² - 10y = -1

Step 2: Complete the Square (x2)

x² - 2x + 1 + y² -10y + 25 = -1 + 1 + 25

(x - 1)² + (y - 5)² = 25

Step 3: Find answers

Center = (h, k)

(1, 5) as Center

Radius = r

r² = 25

r = 5