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

The equation 5x^2 - 6xy + 5y^2 = 16 represents an ellipse.

Determine two points on the ellipse at which the tangent is horizontal.

2. Relevant equations

3. The attempt at a solution

I find the derivative of the equation:

(-10x + 6y) / (-6x + 10y) = 0 iff -10x + 6y = 0, so x = (3/5)y.

Then I sub x back into original equation and get y, I get y = +/- 1/(sqrt(2)), which is wrong.

What did I do wrong?

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# Find two points on an ellpise that have horizontal tangent

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