Answer:
b = 44
Explanation:
We can complete the square(s) to put the equation in standard form. Then we can find the value of b that makes the radius be 7 units.
__
x^2 +y^2 -4x +2y = b . . . . . given
(x^2 -4x) +(y^2 +2y) = b . . . . group by variable
(x^2 -4x +4) +(y^2 +2y +1) = b + 4 + 1 . . . . complete the squares
(x -2)^2 +(y +1)^2 = b +5 = 7^2 = 49 . . . . . write as squares, show radius
b = 49 -5 = 44 . . . . subtract 5
The value of b to make the radius 7 is 44.
_____
The standard form of the equation for a circle is ...
(x -h)^2 +(y -k)^2 = r^2 . . . . . center (h, k), radius r