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# T_T

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

Mar 11, 2021