SOLUTION: What is the standard form of the equation x^2+3y^2+4x+6y+1=0?

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Question 1045637: What is the standard form of the equation x^2+3y^2+4x+6y+1=0?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the standard form of the equation x%5E2%2B3y%5E2%2B4x%2B6y%2B1=0 will be:
x%5E2%2B3y%5E2%2B4x%2B6y%2B1=0......group like terms
%28x%5E2%2B4x%29%2B%283y%5E2%2B6y%29%2B1=0
%28x%5E2%2B4x%29%2B3%28y%5E2%2B2y%29%2B1=0......complete squares

%28x%5E2%2B4x%2Bb%5E2%29-b%5E2%2B3%28y%5E2%2B2y%2Bb%5E2%29-3b%5E2%2B1=0.....recall, %28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2 and in your case for %28x%5E2%2B4x%2Bb%5E2%29 we have a=1 and 2ab=4, so we can find b
2%2A1%2Ab=4->b=4%2F2->b=2
for 3%28y%5E2%2B2y%2Bb%5E2%29 we have a=1 and 2ab=2, so we can find b
2%2A1%2Ab=2->2b=2->b=1
then we have
%28x%5E2%2B4x%2B2%5E2%29-2%5E2%2B3%28y%5E2%2B2y%2B1%5E2%29-3%2A1%5E2%2B1=0
%28x%2B2%29%5E2-4%2B3%28y%2B1%29%5E2-3%2B1=0
%28x%2B2%29%5E2%2B3%28y%2B1%29%5E2-7%2B1=0
%28x%2B2%29%5E2%2B3%28y%2B1%29%5E2-6=0
%28x%2B2%29%5E2%2B3%28y%2B1%29%5E2=6..............both sides divide by 6
%28x%2B2%29%5E2%2F6%2B3%28y%2B1%29%5E2%2F6=6%2F6
%28x%2B2%29%5E2%2F6%2Bcross%283%29%28y%2B1%29%5E2%2Fcross%286%292=1

%28x%2B2%29%5E2%2F6%2B%28y%2B1%29%5E2%2F2=1-> you have an ellipse and this is the standard form of the equation