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

c-   36

taxicab circle radius 9 has 4(9) = 36 points