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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
 #1
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h + k + a + b = (-3) + 1 + 10 + 12 = 20.

 Nov 27, 2019

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