Equation of a hyperbola with some info given

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To find the equation of a hyperbola centered at the origin with a vertical transverse axis, the asymptotes given are 6x + 2y = 0 and 6x - 2y = 0. These can be rewritten to find the slopes, which are ±3. The standard form of a hyperbola with a vertical transverse axis is (y^2)/(a^2) - (x^2)/(b^2) = 1, where the slopes of the asymptotes are ±(a/b). Using the slopes, a/b = 3, allows for the determination of the relationship between a and b. Therefore, the equation can be expressed as y^2/a^2 - x^2/(9a^2) = 1, where a can be any positive value.
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Homework Statement



Write the equatin of the hyperbola whose center is at the origin and has a vertical transverse axis.

Homework Equations


The equations of the asymptotes are 6x+2y=0 and 6x-2y=0



The Attempt at a Solution



I am good at following an example (am an adult who is learning math on own).
However, I cannot find an example like this one and I really have no idea of where to begin.
Could you give me an example that is like this problem worked out and then I will follow it to do this problem? Thanks.
 
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The information given is not enough to define a specific hyperbola. Perhaps the question asked to write the equation of a hyperbola satisfying these conditions.
 
Yes, I think you are right--the directions were to write the equation of a hyperbola satisfying these conditions. Can you help?
 
In general, if a hyperbola has the equation (x^2)/(a^2)-(y^2)/(b^2)=1, then for large x and y, 1 will be negligible, so that we have (x^2)(b^2/a^2)=y^2. In the limit that x and y become "infinite," this defines the relation between the two, and acts as an asymptote.
 

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