SOLUTION: For an algebra project where i have to make a drawing out of different conics, I'm using a hyperbola. Currently, I know the center point, and the slope of the asymptotes, but I'm n

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: For an algebra project where i have to make a drawing out of different conics, I'm using a hyperbola. Currently, I know the center point, and the slope of the asymptotes, but I'm n      Log On


   

Question 1118326: For an algebra project where i have to make a drawing out of different conics, I'm using a hyperbola. Currently, I know the center point, and the slope of the asymptotes, but I'm not really sure how to use the slope of asymptotes to find the rest of my equation.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The center point and the slopes of the asymptotes is not enough information to determine the equation of the hyperbola.

Given the equation of a hyperbola in standard form,

%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2+=+1

The slopes of the asymptotes are b/a and -b/a.

So knowing the slopes of the asymptotes only tells you the ratio of a and b; to know the equation you have to know the specific values of a and b.

Furthermore, note that the slopes of the asymptotes don't tell you whether the branches of the hyperbola open right and left or up and down.