Point of intersection closest to the origin

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How do I find the point of intersection of $ + - + 2 = 0$ and $^2 = ^2 + ^2$ that is closest to the origin?

I know I have to use the LaGrange multiplier in order to minimize the equation $$ (,,) = ^2 + ^2 + ^2. $$ So I have the following:

  • $2 = λ + μ(2)$
  • $2 = λ + μ(2)$
  • $2 = -λ + μ(-2)$
  • $ + - + 2 = 0$
  • $^2 = ^2 + ^2$

But I keep getting that $ = 0$ which has no solution.