(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

x^2 - 2xy + 6y^2 = 10

Find the point on the ellipse closest to the origin (0,0).

2. Relevant equations

3. 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!

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# Homework Help: Calc Optimization - Point on an ellipse closest to origin.

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