Coordinate Geometry: JEE Main 2021 Mathematics question

Let r₁ and r₂ be the radii of the largest and smallest circles, respectively, which pass through the point ($-$4, 1) and having their centres on the circumference of the circle x² + y² + 2x + 4y $-$ 4 = 0. If ${{{r_1}} \over {{r_2}}} = a + b\sqrt 2$, then a + b is equal to :