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Question 27825: I dont get how to find the foci! and i guess it;s crucial for this chapter. hyperbolas stink! how do i find the vertecies foci and the slope of:y^2 over 36 minus x^2 over 4 equals one?? please help me!
Answer by bmauger(101)   (Show Source):
You can put this solution on YOUR website! Unfortunately the answer to the question "I don't understand hyperbolas" can't be answered with a quick answer. You'll probably have to read the chapter in your book a time or two. For some additional information go to: Hyperbola.Wikipedia
Anyway, finding the foci involves finding a, b & c (that's what they're usually called, your book may vary). The equation for a hyperbola is of the format:
 When major axis is y or:
 When major axis is x
In either case the positive term is the major axis, and determines where the foci lie. Frequently h & k will be 0. In any case c is defined by:
 (contrast with the definition of c in an elipse  )
Which reduces to 
The focal points when the major axis is y will be: (k+c, h) and (k-c, h)
and when the major axis is x: (k, h+c) and (k, h-c)
For your problem:
a = 6 (square root of 36)
b = 2 (square root of 4)
c = approximately 6.325
So your foci are at (0, 6.325) and (0, -6.325)
Confused yet? That'll happen. Do some practice problems, read the book, and ask some specific questions if you get stuck again. Also try http://mathworld.wolfram.com/Focus.html for a better explanation of the foci for elipses & hyperbolas.
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