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?