SOLUTION: what is a possible equation for a hyperbola that is centered at the origin, opens left and right and has a transverse axis of length 6

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Question 698158: what is a possible equation for a hyperbola that is centered at the origin, opens left and right and has a transverse axis of length 6
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A hyperbola that is centered at the origin, and opens left and right has an equation of the form
x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1
where x cannot be zero (because it would mean -y%5E2%2Fb%5E2=1<--->y%5E2%2Fb%5E2=-1,
but when y=0, x%5E2%2Fa%5E2=1<--->x%5E2=a%5E2, so x=a or x=-a Those are the x-coordinates of vertices (-a,0) and (a,0),
and the distance between the vertices is the transverse axis = 2a
So the equation you need is
highlight%28x%5E2%2F3%5E2-y%5E2%2Fb%5E2=1%29 or highlight%28x%5E2%2F9-y%5E2%2Fb%5E2=1%29
You can chose a value for b%5E2 to change how "pointy" the vertices are.
The slopes of the asymptotes will be b%2Fa and -b%2Fa