SOLUTION: Write an equation that satifies set of conditions listed below. A hyperbola with foci (0,-sqrt(6))and (0,sqrt(6))and asymptotes y=(sqrt(2)/2) and y=(-sqrt(2)/2)

Question 407470: Write an equation that satifies set of conditions listed below.
A hyperbola with foci (0,-sqrt(6))and (0,sqrt(6))and asymptotes y=(sqrt(2)/2) and y=(-sqrt(2)/2)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Write an equation that satifies set of conditions listed below.A hyperbola with foci (0,-sqrt(6))and (0,sqrt(6))and asymptotes y=(sqrt(2)/2) and y=(-sqrt(2)/2)
..
y=(-sqrt(2)/2)=-1.414x/2
y=(sqrt(2)/2)=1.414x/2
..
given hyperbola has a vertical transverse axis,x=0. (hyperbola opens up and down)
Center is on this line between foci=(0,0)
Asymptotes=+-a/b=sqrt(2)/2
so,a=sqrt(2)
a^2=2
b=2
b^2=4
a and b also represent the legs of a right triangle in which c, the focal point is the hpotenuse.
c^2=a^2+b^2
c=sqrt(2+4)=sqrt(6)
Equation of the hyperbola:
y^2/2+x^2/4=1
The graph will look much like the graph below:
..
y=(((x^2)+4)/2)^.5

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