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Question 719647: Can someone please help..
a hyperbola has vertices (+-5,0) and one focus (6,0) what is the standard form equation of the hyperbola.
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! The standard forms for the equation of a hyperbola is:
 for horizontal hyperbolas; or
 for vertical hyperbolas
The center of a hyperbola is halfway between the vertices. Halfway between (or the midpint of) (-5, 0) and (5, 0) is (0, 0). So the center of the hyperbola is (0, 0). In the standard form, these coordinates are h and k. So h = 0 and k = 0.
The distance between the center and each vertex is called "a". The distance between (0, 0) and either vertex is 5. So a = 5.
The distance between the center and each focus is called "c". The distance between (0, 0) and the one focus we know is 6. So c = 6.
What we need now is "b". The value of b is connected to the values of a and c by the equation:
Using the values we have for and and c this becomes:
The standard form only requires that we know what  is so we will solve for that:
And finally we use the values we have found to write the standard form equation. But which form will we use? The horizontal one or the vertical one? The answer: The horizontal one. Our hyperbola is horizontal because the vertices are on the same horizontal line. (If you can't picture (-5, 0) and (5, 0) in your head, plot them on a graph. You will find that they are to the left and right of each other.) So we will use the standard form for horizontal hyperbolas:
Into this we substitute the values we have found:
which simplifies to:
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