Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and calculations to receive credit. x2 + 4x + y2 − 6y = −4 And please give an explanation.

centre = (- 2, 3 ), radius = 3

Step-by-step 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 + 4x + y² - 6y = - 4

Using the method of completing the square.

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(2)x + 4 + y² + 2(- 3)y + 9 = - 4 + 4 + 9, that is

(x + 2)² + (y - 3)² = 9 ← in standard form

with centre = (- 2, 3 ) and r = = 3