Question 18281: what is the equation of a hyperbola with vertex (6,4) and (6,8) and foci(6,0 and 6,12. i really need an answer for this quickly so any help would be appreciated:-)
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! what is the equation of a hyperbola with vertex (6,4) and (6,8) and foci(6,0) and (6,12).
Mid point of (6,4) & (6,8) is (6,6) : center, and the principal axis is
vertical.
Assume the equation of the hyperbola is:
Set x = 6, y = 4, we have  , so 
(or use dist|(6,4),(6,12)| - dist|(6,4),(6,0)| = 4 = 2a to get a = 2)
Since the distance between two foci (6,0) & (6,12) is 12 = 2c, so c = 6.
by c^2 = a^2 + b^2 = 36,we have b^2 = 32. [Note e = c/a = 3]
Therefore, the equation is
Kenny
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