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Is this a problem in mathematica?


Let's say I wanna solve this problem:

Determine point(s) on y = x^2 +1 that are
closest to (0,2).

So in mathematica:

minDist = (x - 0)^2 + (y - 2)^2;
Minimize[minDist, y == 1 + x^2, {x, y}]

Output will give you: x -> -1/Sqrt[2], y -> 3/2

but x also has another answer: +1/Sqrt[2]. Is this a problem in mathematica or can my code be changed to output the other value of x for the minimum distance?


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