1. A certain ellipse is defined by \(PF_1 + PF_2 = d\).The equation of the ellipse is \(4x^2 - 8x + y^2 + 4y - 8 = 0\). Find d.

2. Let \(F_1 = \left( -3, 1 - \frac{\sqrt{5}}{4} \right)\) and \(F_ 2= \left( -3, 1 + \frac{\sqrt{5}}{4} \right)\). Then the set of points P such that \(|PF_1 - PF_2| = 1\) form a hyperbola. The equation of this hyperbola can be written as \(\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1\).Find h + k + a + b.

Thank you for your help!

Guest Apr 19, 2019