y² = 4x
(2x+b)² - 4x = 0
4x² + 4(b-1)x + b² = 0
x = [-(b-1) ±√(1-2b)]/2
A([-(b-1) +√(1-2b)]/2,1 +√(1-2b))
B([-(b-1) -√(1-2b)]/2,(1-√(1-2b))
|AB|² = [√(1-2b)]² + [2√(1-2b)]² = 5(1-2b) = (3√5)² = 45
b = -4