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Question 748094: what is center and endpoints of major and minor axis and foci
2x^2 + 4y^2 + 4x - 12y = 5
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! what is center and endpoints of major and minor axis and foci
2x^2 + 4y^2 + 4x - 12y = 5
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2x^2 + 4x + 4y^2 - 12y = 5
Complete the Square:
2(x^2+2x+1) + 4(y^2-3y + (9/4)) = 5 + 2 + 9
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2(x+1)^2 + 4(y-(3/2))^2 = 16
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(x+1)^2/8 + (y-(3/2))^2/4 = 1
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center: (1,3/2)
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semi-major axis: sqrt(8) = 2sqrt(2)
semi-minor axis: sqrt(4) = 2
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major axis end-points: (1+2sqrt(2),3/2) and (1-2sqrt(2),3/2)
minor axis end-points: (1,(3/2)+2) and (1,(3/2)-2)
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a^2 = b^2+c^2
c = sqrt[a^2-b^2] = sqrt[8+4] = 2sqrt(3)
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foci: (1+2sqrt(3),3/2) and (1-2sqrt(3),3/2)
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Cheers,
Stan H.
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