SOLUTION: Using the given information to find the equation, in standard form, of the hyperbola. Foci: (6, 0), (-6, 0); Vertices: (5, 0), (-5, 0)

Algebra ->  Finance -> SOLUTION: Using the given information to find the equation, in standard form, of the hyperbola. Foci: (6, 0), (-6, 0); Vertices: (5, 0), (-5, 0)      Log On


   

Question 1121354: Using the given information to find the equation, in standard form, of the hyperbola.
Foci: (6, 0), (-6, 0); Vertices: (5, 0), (-5, 0)
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Clearly the center is at (0,0); and the branches open left and right. So the standard form of the equation is

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

a is the distance from the center to each vertex (5); c is the distance from the center to each focus (6). a, b, and c are related by

c%5E2+=+a%5E2%2Bb%5E2 or, in this problem where a and c are known, b%5E2+=+c%5E2-a%5E2.

So we know a^2=25 and c^2=36, so b^2=11; the equation is

x%5E2%2F25-y%5E2%2F11+=+1