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A simple math problem in senior high school
Let the slope of this tangent be k and pass (0, root number 2).

Then the tangent equation is y root number 2=kx,

That is, kx-y+ radical number 2=0

The distance from the tangent to the center of the circle is 1.

Therefore, d= 1= radical number 2/ radical number (k 2+ 1).

So k 2+1= 2.

So k= 1 or-1.

So the tangent equation is x-y+ radical number 2=0 or x+y- radical number 2=0.