SOLUTION: Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci: (0, -9), (0, 9); vertices: (0, -6), (0, 6)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci: (0, -9), (0, 9); vertices: (0, -6), (0, 6)      Log On


   

Question 1178236: Find the standard form of the equation of the hyperbola satisfying the given conditions.
Foci: (0, -9), (0, 9); vertices: (0, -6), (0, 6)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

As the vertices are (0, -6) and (0, 6), the center is at (0.0)
The hyperbola opens up and down , we need
-x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1
the vertices are 6 unitc from the center, thus
b+=+6
The foci are 9 units from the center. The distance to the focus is c.
c=9
a%5E2+%2B+b%5E2+=+c%5E2
Thus,
a%5E2+=+c%5E2+-+b%5E2+=81+-+36+=+45

Equation of the hyperbola:
-x%5E2%2F45%2By%5E2%2F36=1