Answer:
(3, -1); 4
Step-by-step explanation:
x² + y² - 6x + 2y = 6
Strategy:
Convert the equation to the centre-radius form:
(x - h)² + (y - k)² = r²
The centre of the circle is at (h, k) and the radius is r
Solution:
Keep the x- and y-terms together.
x² - 6x + y² + 2y = 6
1. Complete the square for x
(Take half the coefficient of x, square it, and add to each side of the equation)
(x² - 6x + 9) + y² + 2y = 15
2. Complete the square for y
(x² - 6x + 9) + (y² + 2y + 1) = 16
3. Express the result as the sum of squares
(x - 3)² + (y + 1)² =4²
h = 3; k = -1; r = 4
The centre of the circle is at (3, -1) and the length of the radius is 4.
The graph of the circle below has its centre at (3, -1) and radius 4.
