SOLUTION: 2x^2+y^2=2+4(x-y), find the center, vertices and the length of the major and minor axes of the ellipse.

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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.
Answer by lwsshak3(11628) About Me  (Show Source):
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2x^2+y^2=2+4(x-y), find the center, vertices and the length of the major and minor axes of the ellipse.
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2x^2+y^2=2+4(x-y)
2x^2+y^2=2+4x-4y
2x^2-4x+y^2+4y=0
complete the square:
2(x^2-2x+1)+(y^2+4y+4)=0+2+4
2(x-1)^2+(y+2)^2=6
(x-1)^2/3+(y+2)^2/6=1
This is an equation of an ellipse with vertical major axis.
Its standard form: %28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1
center: (1,-2)
a^2=6
a=√6≈2.4
length of major axis=2a=2√6
b^2=3
b=√3≈1.73
length of minor axis=2b=2√3
vertices: (1, -2±a)=(1, -2±2.4)=(2,-4.4) and (2, 0.4)