SOLUTION: Find the equation of the hyperbola for each given conditions. a. Vertices at (o,3) and (0,-3) and a focus at (0,5).

Algebra ->  Finance -> SOLUTION: Find the equation of the hyperbola for each given conditions. a. Vertices at (o,3) and (0,-3) and a focus at (0,5).       Log On


   



Question 1191089: Find the equation of the hyperbola for each given conditions.
a. Vertices at (o,3) and (0,-3) and a focus at (0,5).

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1
given:

Vertices at (0,3) and (0,-3)
a focus at (0,5)
in your case the transverse axis lies on the y-axis, the vertices are located at (0a), and the foci are located at (0c)
=>a=3
=> c=5
Center is half way between, at (0,0)=>h=0, k=0
in this case your equation is of the form:
y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1
find a can be found using this formula:
b%5E2+=+c%5E2+-+a%5E2
b%5E2+=+25+-+9
b%5E2+=+16
b=4+


equation is:
y%5E2%2F9-x%5E2%2F16=1