What is the radius of the circle defined by x2 + 2x + y2 + 6y - 39 = 0?

49

9

7

81

7 units

Step-by-step explanation:

(h, k) = (-2/2, - 6/2) = (-1,-3)

(-1) ² + (-3) ² - (-39) = r²

49 = r²

r = 7

radius = 7

the equation of a circle in standard form is

(x-a) ² + (y-b) ² = r²

where (a, b) are the coordinates of the centre and r is the radius

To obtain this form ' complete the square ' on both the x and y terms

x² + 2 (1) x + 1 + y² + 2 (3) y + 9 = 39 + 1 + 9

(x+1) ² + (y+3) ² = 49 ← in standard form

with centre (1, 3) and r = √49 = 7