$x$ and $y$ are real numbers where satisfied the equation $x^2+y^2+xy-3x-3y-9=0$
Find the max. and min. values of $x^2+y^2$
I don't know how to find the constraint
Your constraint is the curve $$x^2+y^2+xy-3x-3y-9=0$$ Hence, you need to consider the function $$f(x,y; \lambda) = x^2 + y^2 + \lambda (x^2+y^2+xy-3x-3y-9)$$ and differentiate with respect to $x,y$ and $\lambda$ and find the critical points.