SOLUTION: Write an equation of the hyperbola that meets the following conditions: the vertices are at (-2,-3) and (6,-3) foci is at (-4,-3)

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Question 860236: Write an equation of the hyperbola that meets the following conditions:
the vertices are at (-2,-3) and (6,-3)
foci is at (-4,-3)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The question is most comfortably answered using knowledge of standard form for a hyperbola.

The subtraction is on the y%5E2 term, as indicated by the line containing the vertices.

Center is (2,-3).
a=%286-%28-2%29%29%2F2=4.
c is how far from center to the focus;
c=2-%28-4%29=6.
The way that a, b, and c are related is a%5E2%2Bb%5E2=c%5E2.
b%5E2=c%5E2-a%5E2
b%5E2=36-16
b%5E2=20, to be used just as that.

Fill the numeric information into standard form.
highlight%28%28x-2%29%5E2%2F16-%28y%2B3%29%5E2%2F20=1%29

Check your textbook for discussion about the details; or also check the article, http://en.wikipedia.org/wiki/Hyperbola