Answer:
(centre = (3, - 1 ) and radius = 7
Explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² - 6x + 2y - 39 = 0 ( collect x/ y terms and add 39 to both sides )
x² - 6x + y² + 2y = 39
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 3)x + 9 + y² + 2(1)y + 1 = 39 + 9 + 1
(x - 3)² + (y + 1)² = 49 ← in standard form
with centre (3, - 1 ) and r =
= 7