document.write( "Question 851918: 2x^2+y^2=2+4(x-y), find the center, vertices and the length of the major and minor axes of the ellipse. \n" ); document.write( "
Algebra.Com's Answer #513082 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
2x^2+y^2=2+4(x-y), find the center, vertices and the length of the major and minor axes of the ellipse.
\n" ); document.write( "***
\n" ); document.write( "2x^2+y^2=2+4(x-y)
\n" ); document.write( "2x^2+y^2=2+4x-4y
\n" ); document.write( "2x^2-4x+y^2+4y=0
\n" ); document.write( "complete the square:
\n" ); document.write( "2(x^2-2x+1)+(y^2+4y+4)=0+2+4
\n" ); document.write( "2(x-1)^2+(y+2)^2=6
\n" ); document.write( "(x-1)^2/3+(y+2)^2/6=1
\n" ); document.write( "This is an equation of an ellipse with vertical major axis.
\n" ); document.write( "Its standard form: \"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"
\n" ); document.write( "center: (1,-2)
\n" ); document.write( "a^2=6
\n" ); document.write( "a=√6≈2.4
\n" ); document.write( "length of major axis=2a=2√6
\n" ); document.write( "b^2=3
\n" ); document.write( "b=√3≈1.73
\n" ); document.write( "length of minor axis=2b=2√3
\n" ); document.write( "vertices: (1, -2±a)=(1, -2±2.4)=(2,-4.4) and (2, 0.4) \n" ); document.write( "
\n" );