How can I optimize f(x,y) bound to g(x,y) = 11?

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How can I optimize this? I think it was solved using lagrange multipliers but don't know how to continue!

f(x,y)=x^2+y^2 g(x,y)=xy+10

In the final part of Find the Vectorial Equation of the intersection between surfaces $f(x,y) = x^2 + y^2$ and $g(x,y) = xy + 10$

Thanks!

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No need for Lagrande multipliers: $$g(x,y)=11\iff xy=1\iff x=\frac1y.$$ Now plug this into $f$. You will obtain a function in a single variable, which you can then mimize using the classical method of taking the derivative and setting it equal to zero.