SOLUTION: I am having trouble with hyperbolas. Please help me determine the foci and equations of the asymptotes of: 9x^2-25y^2=225. Thanks for your help.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I am having trouble with hyperbolas. Please help me determine the foci and equations of the asymptotes of: 9x^2-25y^2=225. Thanks for your help.      Log On


   

Question 64981: I am having trouble with hyperbolas. Please help me determine the foci and equations of the asymptotes of: 9x^2-25y^2=225. Thanks for your help.
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Equation of a Hyperbola; Center at (0,0); Foci at (+\-c,0); Vertices at (+\-a,0); Transverse axis along the x-axis. Two oblique asymptotes at y=+\-(b/a)x:
highlight%28x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1%29, where b%5E2=c%5E2-a%5E2
Determine the foci and equations of the asymptotes of: 9x%5E2-25y%5E2=225.
9x%5E2%2F225-25y%5E2%2F225=225%2F225
x%5E2%2F25-y%5E2%2F9=1
x%5E2%2F5%5E2-y%5E2%2F3%5E2=1
a=5 and b=3
b%5E2=c%5E2-a%5E2---> 3%5E2=c%5E2-5%5E2
9=c%5E2-25
9%2B25=c%5E2-25%2B25
34=c%5E2
%2B-sqrt%2834%29=c
Therefore the foci (+\-c,0) are: (-sqrt%2834%29,0) and (sqrt%2834%29,0)
The equations of the asymptotey=+\-(b/a)x are: y=-%283%2F5%29x and y=%283%2F5%29x
Happy Calculating!!!