Find two points on an ellpise that have horizontal tangent

[zeion]

Homework Statement

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

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

Homework Equations

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?

 

[ehild]

so x = (3/5)y.

This is correct...

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?

Something with the back substitution into the original equation.

ehild

 

[zeion]

Got it, thanks.