SOLUTION: (x-2)^2-(x-2)(y+1)+(y+1)^2=27 Can you help me find what x and y will equal

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Question 384055: (x-2)^2-(x-2)(y+1)+(y+1)^2=27
Can you help me find what x and y will equal
Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-2%29%5E2-%28x-2%29%28y%2B1%29%2B%28y%2B1%29%5E2=27
%28x%5E2-4x%2B4%29-%28xy%2Bx-2y-2%29%2B%28y%5E2%2B2y%2B1%29=27
x%5E2-4x%2B4-xy-x%2B2y%2B2%2By%5E2%2B2y%2B1=27
x%5E2-xy-5x%2B2y%2By%5E2%2B4y%2B7=27
x%5E2-xy-5x%2B2y%2By%5E2%2B4y-20=0
.
.
The general equation for a conic section is,
Ax2+%2B+Bxy+%2B+Cy2+%2B+Dx+%2B+Ey+%2B+F+=+0
In this case,
A=1
B=-1
C=1
D=-5
E=4
F=-20
B%5E2-4AC=1-4%281%29%281%29=-3
So this not a parabola or a hyperbola.
It turns out to be the equation of an off axis ellipse.
It does have several integer solutions,
(-4,-4)
(-1,-7)
(-1,2)
(5,-4)
(5,5)