What is the x coordinate of the center of a circle equation is x^2 + y^2 + 4x - 6y = b

x = - 2

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

To obtain this form use the method of completing the square

Given

x² + y² + 4x - 6y = b (collect x and y terms together)

x² + 4x + y² - 6y = b

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

x² + 2 (2) x + 4 + y² + 2 ( - 3) y + 9 = b + 4 + 9

(x + 2) ² + (y - 3) ² = b + 13 ← in standard form

with (h, k) = ( - 2, 3)

Thus x - coordinate of centre is x = - 2