Let \(F_1 = (0,1) \) and \(F_ 2= (4,1) \). Then the set of points such that \(PF_1 + PF_2 = 6\) form an ellipse. The equation of this ellipse can be written as \(\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1.\) Find \(h + k + a + b.\)
$h + k + a + b = 8 + 2 \sqrt{3}$.
