SOLUTION: Write the equation of the hyperbola . Vertices: (0, 2), (0, - 2) Focus : (0, 6)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equation of the hyperbola . Vertices: (0, 2), (0, - 2) Focus : (0, 6)      Log On


   



Question 1187216: Write the equation of the hyperbola . Vertices: (0, 2), (0, - 2) Focus : (0, 6)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the equation of the hyperbola:
given:
Vertices: (0,+2), (0, -+2)
Focus : (0,+6)
since transverse axis parallel to the y-axis, equation is
%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1
Center is half way between vertices: (h,k)=(%280%2B0%29%2F2,%282-2%29%2F2)=(0,0) => h=0, k=0

the coordinates of the vertices are (0, ± a)=(0, 2)=>a=2
the coordinates of the foci are (0c)=(0, 6) =>c=6
find b
6%5E2=2%5E2%2Bb%5E2
b%5E2=6%5E2-2%5E2
b%5E2=36-4
b%5E2=32

and your equation is:
%28y-0%29%5E2%2F4-%28x-0%29%5E2%2F32=1
y%5E2%2F4-x%5E2%2F32=1