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# Hyperbola Question Help

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Let $$F_1 = \left( -3, 1 - \frac{\sqrt{5}}{4} \right)$$ and $$F_ 2= \left( -3, 1 + \frac{\sqrt{5}}{4} \right)$$ (foci).  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

$$\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1$$

where $$a, b > 0.$$ Find $$h + k + a + b.$$

Jul 31, 2019