You provided the equation:

$x^2 + xy + y^2 = 6$

Would you like to:

• Solve for one variable in terms of the other?
• Find the points that satisfy this equation (e.g., by graphing)?
• Perform implicit differentiation to find the rate of change between $x$ and $y$?

Let me know what you'd like to explore!

Questions:

1. Would you like to solve for $x$ in terms of $y$ or vice versa?
2. Are you interested in graphing the equation?
3. Should we solve for specific points on the curve?
4. Would you like to use implicit differentiation to find $\frac{dy}{dx}$?
5. Are you exploring this as part of a specific mathematical topic (e.g., conic sections)?

Tip: Implicit differentiation is useful when both $x$ and $y$ are variables, and it reveals how one changes relative to the other.