SOLUTION: Y^2 − x^2 /4 = 1.What are all the vertices,asymptotes, foci and hyperbola?

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Question 962170: Y^2 − x^2 /4 = 1.What are all the vertices,asymptotes, foci and hyperbola?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2-+x%5E2%2F4+=+1 .....=> here you have %28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1 where k=0 and h=0
When the transverse axis is vertical (or, when the center, foci, and vertices line up above and below each other, parallel to the y-axis), then the a%5E2 goes with the y part of the hyperbola's equation, and the x part is subtracted.
since k=0 and h=0, the center is at (0, 0)
a%5E2=1 =>semimajor axis length 1
b%5E2=4 => semiminor axis length +2
asymptotes' equations:
y=± a%2Fb%28x-h%29%2Bk
y=± 1%2F2%28x-0%29%2B0
y=±+%281%2F2%29x=>asymptotes are y=+%281%2F2%29x and y=-%281%2F2%29x
vertices:
(0, -1)
(0, 1)

c%5E2=a%5E2%2Bb%5E2=1%2B4=5
c=sqrt%285%29
so, foci is at:
(0, -sqrt%285%29)
(0, sqrt%285%29)
or
(0,+-2.24)
(0, 2.24)
the "eccentricity"+e, where e+=+c%2Fa is e=sqrt%285%29 or e=2.24