Moving along a Circle

Geometry Level 2

For point (x,y)(x,y) moving along the circle x2+y2=4x^2+y^2=4, let aa and bb be the maximum and minimum values, respectively, of 11+x2+11+y2.\frac{1}{1+x^2}+\frac{1}{1+y^2}. What is the value of abab?

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