SOLUTION: Hi. I am having a very tough time with the conic sections portion of my algebra class. Is there anyway someone can help me solve the equation: Find an equation for the hyperbola

Question 1136851: Hi. I am having a very tough time with the conic sections portion of my algebra class. Is there anyway someone can help me solve the equation:
Find an equation for the hyperbola with vertices at (0, -6) and (0, 6); asymptote the line y=3/5x
any help would be sincerely grateful!
Thank you in advance for any help!
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Clearly there are two asymptotes; if the equation of one of them is y=(3/5)x, then the equation of the other is y = (-3/5)x.

The coordinates of the vertices, and also the fact that the asymptotes pass through the origin, tell us that the center of the hyperbola is at the origin.

And the vertices on the y-axis tell us that the branches of the hyperbola open up and down.

The standard form of the equation of a hyperbola with center at the origin and branches opening up and down is

a is the distance from the center to each vertex, so you know a; all you need to finish the equation is b.

For that, use the fact that the slopes of the asymptotes are a/b and -a/b.

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