SOLUTION: Classify the conic section and write its equation in standard form. x^2-4y^2-6x-16y+29=0

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Question 970906: Classify the conic section and write its equation in standard form.
x^2-4y^2-6x-16y+29=0
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-4y^2-6x-16y+29=0
rewrite
x^2-6x -4y^2-16y = -29
rewrite
x^2-6x - 4(y^2+4y) = -29
complete the square
x^2-6x+9- 4 (y^2+4y+4) = -29 + 9 (from x) -16 (from y) = -36
(x-3)^2 - 4(y+2)^2 =-36
Divide by 36
[(x-3)^2/36} - [(y+2)^2]/9 = -1
This is a hyperbola.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-4y%5E2-6x-16y%2B29=0
%28x%5E2-6x%29-%284y%5E2%2B16y%29%2B29=0.....complete square
%28x%5E2-6x%2Bb%5E2%29-b%5E2-4%28y%5E2%2B4y%2Bb%5E2%29-b%5E2%2B29=0...recall the rule %28a-b%29%5E2=a%5E2-2ab%2Bb%5E2
in your case (for x) a=1, and 2ab=6=>2%2A1b=6=>b=3
and (for x) a=1, and 2ab=4=>2%2A1b=4=>b=2
so, we have
%28x%5E2-6x%2B3%5E2%29-3%5E2-4%28y%5E2%2B4y%2B2%5E2%29-%28-4%29%2A2%5E2%2B29=0
%28x-3%29%5E2-9-4%28y%2B2%29%5E2%2B16%2B29=0
%28x-3%29%5E2-4%28y%2B2%29%5E2%2B16%2B29-9=0
%28x-3%29%5E2-4+%28y%2B2%29%5E2%2B36+=+0........both sides divide by -36
%28x-3%29%5E2%2F-36-4+%28y%2B2%29%5E2%2F-36%2B36%2F-36+=+0
-%28x-3%29%5E2%2F36%2B+%28y%2B2%29%5E2%2F9-1+=+0
%28y%2B2%29%5E2%2F9-%28x-3%29%5E2%2F36=1