document.write( "Question 384055: (x-2)^2-(x-2)(y+1)+(y+1)^2=27
\n" ); document.write( "Can you help me find what x and y will equal \n" ); document.write( "

Algebra.Com's Answer #271901 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28x-2%29%5E2-%28x-2%29%28y%2B1%29%2B%28y%2B1%29%5E2=27\"$
\n" ); document.write( " $\"%28x%5E2-4x%2B4%29-%28xy%2Bx-2y-2%29%2B%28y%5E2%2B2y%2B1%29=27\"$
\n" ); document.write( " $\"x%5E2-4x%2B4-xy-x%2B2y%2B2%2By%5E2%2B2y%2B1=27\"$
\n" ); document.write( " $\"x%5E2-xy-5x%2B2y%2By%5E2%2B4y%2B7=27\"$
\n" ); document.write( " $\"x%5E2-xy-5x%2B2y%2By%5E2%2B4y-20=0\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "The general equation for a conic section is,
\n" ); document.write( " $\"Ax2+%2B+Bxy+%2B+Cy2+%2B+Dx+%2B+Ey+%2B+F+=+0\"$
\n" ); document.write( "In this case,
\n" ); document.write( " $\"A=1\"$
\n" ); document.write( " $\"B=-1\"$
\n" ); document.write( " $\"C=1\"$
\n" ); document.write( " $\"D=-5\"$
\n" ); document.write( " $\"E=4\"$
\n" ); document.write( " $\"F=-20\"$
\n" ); document.write( " $\"B%5E2-4AC=1-4%281%29%281%29=-3\"$
\n" ); document.write( "So this not a parabola or a hyperbola.
\n" ); document.write( "It turns out to be the equation of an off axis ellipse.
\n" ); document.write( "It does have several integer solutions,
\n" ); document.write( "(-4,-4)
\n" ); document.write( "(-1,-7)
\n" ); document.write( "(-1,2)
\n" ); document.write( "(5,-4)
\n" ); document.write( "(5,5) \n" ); document.write( "

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