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)

Algebra ->  Finance -> 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)       Log On


   

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) About Me  (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

y%5E2%2Fa%5E2-x%5E2%2Fb%5E2+=+1

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

c%5E2+=+a%5E2%2Bb%5E2

or, for this problem,

b%5E2+=+c%5E2-a%5E2

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

So the equation of the hyperbola is

y%5E2%2F9-x%5E2%2F16+=+1