SOLUTION: I am not sure how to go about changing the following problem into standard form. I tried to do completing the square, but I'm not sure how to use it in this situation or when ther

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I am not sure how to go about changing the following problem into standard form. I tried to do completing the square, but I'm not sure how to use it in this situation or when ther      Log On


   

Question 49056: I am not sure how to go about changing the following problem into standard form. I tried to do completing the square, but I'm not sure how to use it in this situation or when there is a coefficient other than 1 in front of x^2 and y^2. I would greatly appreciate help on how to solve the following problem. Thanks!
Change the equation to standard form and name the figure.
3x^2-2y^2-12x-20y-44=0
Found 2 solutions by Nate, xerxes0212:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+-+2y%5E2+-+12x+-+20y+-+44+=+0
3x%5E2+-+12x+-+2y%5E2+-+20y+=+44
3%28x%5E2+-+4x%29+-+2%28y%5E2+%2B+10y%29+=+44
3%28x%5E2+-+4x%29+-+2%28y%5E2+%2B+10y%29+=+44
3%28x+-+2%29%5E2+-+2%28y+%2B+5%29%5E2+=+44+%2B+4%2A3+%2B+25%2A2 You square the number, then multiply it by the coefficient.
3%28x+-+2%29%5E2+-+2%28y+%2B+5%29%5E2+=+106
%28x+-+2%29%5E2%2F%28106%2F3%29+-+%28y+%2B+5%29%5E2%2F53+=+1

Answer by xerxes0212(2) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2 - 2y^2 - 12x - 20y - 44 = 0
Transpose -44 to the other side.
3x^2 - 2y^2 - 12x - 20y = 44
Rearrange the terms.
3x^2 - 12x - 2y^2 - 20y = 44
Factor expressions with same variables by finding the common factor.
3(x^2 - 4x) - 2(y^2 + 10y) = 44
Use completing the squares and balance the equation (add terms to the right side) by adding the terms that were added to the left side.
3(x^2 - 4x + 4) - 2(y^2 + 10y + 25) = 44 + 3(4) - 2(25)
Simplify the right side.
3(x^2 - 4x + 4) - 2(y^2 + 10y + 25) = 6
Write the perfect square trinomials as square of binomials.
3(x - 2)^2 - 2(y+ 5)^2 = 6
Make the right side equal to 1 by dividing all terms by 6.
(x - 2)^2 - (y + 5)^2
--------- --------- = 1
2 3
This equation represents a hyperbola with vertical traverse axis.