Answer:
Step-by-step explanation:
Part A
Given equation of the circle is,
x² + y² - 4x + 2y = b
Standard equation of the circle is given by,
(x - h)² + (y - k)² = r²
Here, (h, k) is the center and r = radius of the circle
Now we will convert this equation into a standard equation of the circle,
x² - 4x + y² + 2y = b
x² - 2(2x) + 2² + y² + 2y + 1² = b + 2² + 1²
(x² - 2(2x) + 4) + (y² + 2y + 1) = b + 4 + 1
(x - 2)² + (y + 1)² = √(b + 5)²
Therefore, (2, -1) will be the center of the given circle.
y-coordinate of the circle = -1
Part B
Since, radius of the circle is 7 units,
Therefore, [tex]\sqrt{b+5}=7[/tex]
b + 5 = 49
b = 49 - 5
b = 44
