Minimise  subject to  

To minimize f(x,y) = (x-1)^2 + y^2 subject to g(x,y) = y^2 -4x = 0, we can use the method of Lagrange multipliers.

Let L(x,y,λ) = f(x,y) - λg(x,y) be the Lagrangian function, where λ is the Lagrange multiplier.

Then we have:

L(x,y,λ) = (x-1)^2 + y^2 - λ(y^2 - 4x)

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