SOLUTION: Simplify the hyperbola 36x^2-4y^2+216x-40y+80

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Question 738317: Simplify the hyperbola 36x^2-4y^2+216x-40y+80
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

36x%5E2-4y%5E2%2B216x-40y%2B80=0
first complete the square :
36x%5E2-4y%5E2%2B216x-40y%2B80+=+0...group like terms
%2836x%5E2%2B216x%29-%284y%5E2%2B40y%29%2B80+=+0...factor
36%28x%5E2%2B6x%29-4%28y%5E2%2B10y%29%2B80+=+0.....complete the square
36%28x%5E2+%2B+6x+%2B+____%29+-+4%28y%5E2+%2B+10y+%2B+____%29+=+-80
36%28x%5E2+%2B+6x+%2B+9%29+-324-+4%28y%5E2+%2B10y+%2B+25%29-%28-4%2A25%29+=+-80
36%28x%5E2+%2B+6x+%2B+9%29+-324-+4%28y%5E2+%2B10y+%2B+25%29%2B100+=+-80
36%28x%5E2+%2B+6x+%2B+9%29+-+4%28y%5E2+%2B10y+%2B+25%29+=+-80%2B324-100
36%28x%5E2+%2B+6x+%2B+9%29+-+4%28y%5E2+%2B10y+%2B+25%29+=+144
36+%28x%2B3%29%5E2-4+%28y%2B5%29%5E2-144=0