SOLUTION: How do I solve the equation 4x^2 - 9y^2 = 9 for a hyperbola when I can not make it fit the standard form of x^2/a - y^2/b = 1 because of the 4 and 9. Any help is appreciated

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: How do I solve the equation 4x^2 - 9y^2 = 9 for a hyperbola when I can not make it fit the standard form of x^2/a - y^2/b = 1 because of the 4 and 9. Any help is appreciated      Log On


   

Question 296335: How do I solve the equation 4x^2 - 9y^2 = 9 for a hyperbola when I can not make it fit the standard form of x^2/a - y^2/b = 1 because of the 4 and 9. Any help is appreciated
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
By "solve" you probably mean "write in standard form" %28x%5E2%2Fa%5E2%29-%28y%5E2%2Fb%5E2%29+=+1 This is the standard form of an equation of a hyperbola with center at (0, 0) and vertices on the x-axis.
4x%5E4-9y%5E2+=+9 Divide both sides by 9.
%284%2F9%29x%5E2-y%5E2+=+1 Notice that 4%2F9+=+%282%2F3%29%5E2 and %282%2F3%29%5E2+=+1%2F%283%2F2%29%5E2 so you can rewrite the first term:
%28x%5E2%2F%283%2F2%29%5E2%29-y%5E2+=+1
Comparing this with:
x%5E2%2Fa%5E2+-+y%5E2%2Fb%5E2+=+1 you can see that:
a+=+%283%2F2%29 and b+=+1