Question 1153742: Write an equation of a hyperbola with the given foci and vertices
Foci (0,+-13), vertices (0,+-5)
Answer by MathLover1(20850)   (Show Source):
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given:
foci ( , ), (, )
vertices (, ), (, )
We can tell that it is a vrtical hyperbola.
The center point is (, ).
To find  , we'll count from the center to either vertex.
To find  , we'll count from the center to either focus.
then use
We have all our information: ,  , ,  . Since it's a horizontal hyperbola centered in origin, we'll choose that formula and substitute in our information.
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