SOLUTION: I just don't get these problems and need help please. Which conic section is represented by this equation? 9x^2-36x-4y^2-24y-36=0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I just don't get these problems and need help please. Which conic section is represented by this equation? 9x^2-36x-4y^2-24y-36=0      Log On


   

Question 64312: I just don't get these problems and need help please.
Which conic section is represented by this equation?
9x^2-36x-4y^2-24y-36=0
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the conic section represented by:
9x%5E2-36x-4y%5E2-24y-36+=+0 First, add 36 to both sides of the equation.
9x%5E2-36x-4y%5E2-24y+=+36 Now group the x-terms and the y-terms.
%289x%5E2-36x%29+-+%284y%5E2+%2B+24y%29+=+36 Next, factor a 9 from the x-group and a 4 from the y-group.
9%28x%5E2-4x%29+-+4%28y%5E2%2B6y%29+=+36 Divide both sides by 36.
9%28x%5E2-4x%29%2F36+-+4%28y%5E2%2B6y%29%2F36+=+1 Simplify the left side.
%28%28x%5E2-4x%29%29%2F4+-+%28%28y%5E2%2B6y%29%29%2F9+=+1 Now complete the squares in the x-terms and the y-terms.
%28%28x%5E2-4x%2B4%29%29%2F4+-+%28%28y%5E2%2B6y%2B9%29%29%2F9+=+1 NB: When we added the 4 to the x-terms, we really added 4/4 = 1. And when we added the 9 to the y-terms we really added -9/9 = -1, so the net result is we added 0 to the left side.
Now we need to factor the x-terms and the y-terms.
%28%28x-2%29%5E2%29%2F2%5E2+-+%28%28y%2B3%29%5E2%29%2F3%5E2+=+1
Compare this with the standard form for an hyperbola whose centre is at (h, k)
%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1
In your equation, h = 2, k = -3, a = 2, b = 3