SOLUTION: Using the given information to find the equation, in standard form, of the hyperbola. Foci: (0, 5), (0, -5); Vertices: (0, 3), (0, -3)

Question 1121382: Using the given information to find the equation, in standard form, of the hyperbola.
Foci: (0, 5), (0, -5); Vertices: (0, 3), (0, -3)

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The given coordinates of the vertices and foci tell us that the branches of the hyperbola open up and down, and that the center is (0,0). So the general form of the equation is

a is the distance from the center to each vertex; so a=3.

c is the distance from the center to each focus; so c = 5.

For a hyperbola, a, b, and c are related by

or, for this problem,

Since c=5 and a=3, b=4.

So the equation of the hyperbola is

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