SOLUTION: The problem is 9y^2+18y=25x^2+216 I have tried over and over to solve this and I keep getting odd numbers. I do not know how to get it into standard form correctly or get a, b,

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The problem is 9y^2+18y=25x^2+216 I have tried over and over to solve this and I keep getting odd numbers. I do not know how to get it into standard form correctly or get a, b,       Log On


   

Question 564980: The problem is 9y^2+18y=25x^2+216
I have tried over and over to solve this and I keep getting odd numbers. I do not know how to get it into standard form correctly or get a, b, or c to graph it. Help!!
Thank you,
Kaite
Answer by issacodegard(60) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, the equation of a hyperbola is
%28X%5E2%29%2F%28a%5E2%29-%28Y%5E2%29%2F%28b%5E2%29=1
So, consider the left hand side of the equation given in the problem. We can complete the square by adding 9 to both sides. This gives us:
9%28y%2B1%29%5E2=25x%5E2%2B225
Rearranging, and letting X=x, Y=y+1, we get:
%28X%5E2%29%2F%28225%2F25%29-%28Y%5E2%29%2F%28225%2F9%29=1
This is the equation of a hyperbola for say z and w:
%28z%5E2%29%2F%28225%2F25%29-%28w%5E2%29%2F%28225%2F9%29=1
Shifted one unit down (we would need to take w=y+1 to get the equation given in X,Y)