- #1
jbot97
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Homework Statement
x^2 - 2xy + 6y^2 = 10
Find the point on the ellipse closest to the origin (0,0).
Homework Equations
The Attempt at a Solution
Absolutely no one in my class can solve this. We've been to the math lab and none of the helpers there know how to solve it. I think the only person who knows how to solve it here is my professor, and he essentially dodges our requests for an example. I know how to solve this if the ellipse is, for example, x^3+4y^2 = 7. The problem is, this ellipse has 2xy in it and I don't know how to solve for y to plug in the distance formula.For x^3 + 4y^2 = 10:
y = [(10-x^3)/4]^.5
D = sq rt {x^2 + [(10-x^3)^.5]^2}
When D is a min, you have the closest point to the origin.
So, I essentially just need to know how to solve x^2 - 2xy + 6y^2 = 10 for y, or an alternate means to solve this problem.
Thanks!