SOLUTION: An ellipse passing through (2, 3) and (6, 1)?

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Question 1042880: An ellipse passing through (2, 3) and (6, 1)?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the genereal equation of an ellipse,
Cx%5E2%2BDy%5E2=1
Use each point to get a linear equation,
C%282%29%5E2%2BD%283%29%5E2=1
1.4C%2B9D=1
and
C%286%29%5E2%2BD%281%29%5E2=1
2.36C%2BD=1
Multiply eq. 2 by 9 and subtract eq. 1 from it,
324C%2B9D-4C-9D=9-1
320C=8
C=8%2F320
C=1%2F40
Then,
4%281%2F40%29%2B9D=1
1%2F10%2B9D=1
9D=1-1%2F10
9D=9%2F10
D=1%2F10
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x%5E2%2F40%2By%5E2%2F10=1
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