SOLUTION: Hi, there! I'm a Brazilian engineering student. I'm kind of stuck with a problem in pre-calc about a conic equation. The problem ask me to identify the conic section of the followi

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Question 851916: Hi, there! I'm a Brazilian engineering student. I'm kind of stuck with a problem in pre-calc about a conic equation. The problem ask me to identify the conic section of the following equation:
3x^2 - 2y^2 + 18x - 4y + 20 = 0
I went throught the algebra stuff (did by completing the square in x and y) but then i got stuck in...
[3*(x + 3)^2] / 5 - [2*(y + 1)^2] / 5 = 1
How can i proceed with it? The answer in my book says it is an hyperbola with the equation...
[(x + 3)^2] / 2 - [(y + 1)^2] / 3 = 1
What bothers me is the 3/5 and the -2/5 that i found on those binomials. An hyperbola equation isn't suppose to have a number on the numerators, isn't?
So, i would be glad if someone could tell me how to proceed with or if i did something wrong.
Found 2 solutions by richwmiller, josh_jordan:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
It is a hyperbola.
3(x+3)^2-2(y+1)^2=5 with center at -3,-1

Answer by josh_jordan(263) (Show Source):
You can put this solution on YOUR website!
Hello. You need to rewrite each fraction without the 3 and without the 2 in the numerators. When you do this, you will end up with:

However, the denominators are fractions and are not perfect squares. I am unsure how they came up with , unless I'm missing something...