SOLUTION: I am unsure on how to solve a problem such as: {{{ 3x^2+7y^2-12x-28y= -19 }}} if possible can you help me solve this problem as well as explain how to solve others similar to

Question 699338: I am unsure on how to solve a problem such as:

if possible can you help me solve this problem as well as explain how to solve others similar to it?
Thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!

3x^2+7y^2-12x-28y = -19
--------
Rearrange:
3x^2-12x+? +7y^2-28y+? = -19
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Complete the square on the "x" and on the "y" terms:
3(x^2-4x+4) + 7(y^2-4y+4) = -19 + 3*4+7*4
-------------------------------
Factor:
3(x-2)^2 + 7(y-2)^2 = 21
----
Standardize:
(3/21)(x-2)^2 + (7/21)(y-2)^2 = 1
(x-2)^2/7 + (y-2)/3 = 1
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This is an ellipse with center at (2,2),
semi-major axis: sqrt(7)
semi-minor axis: sqrt(3)
============================
Cheers,
Stan H.
=================
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