Using the following equation, find the center and radius: x² - 2x + y² - 6y = 26

Solution:

The general equation of a circle is given by:

(x - h)² + (y - k)²= r² --- (1)

The circle represented by the above equation is of radius r and centered at coordinates (h, k)

The given equation x² - 2x + y² - 6y = 26 can be converted into the equation form given in (1) above.

x²- 2x + y² - 6y = 26

Adding 1 and 9 on both sides of the equality we get:

(x² - 2x + 1) + (y² - 6y + 9) = 26 + 1 + 9

(x - 1)² + (y - 3)² = 36

(x - 1)² + (y - 3)² = 6² --- (2)

Equation (2) now represents a circle with

Radius r = 6 and centered at coordinates (1, 3)

Using the following equation, find the center and radius: x² - 2x + y² - 6y = 26

Summary:

The equation x² - 2x + y² - 6y = 26 represents a circle centered at (1, 3) and has a radius ‘r’ = 6.