The slope of the tangent to a curve C : y = y(x) at any point (x, y) on it is \(\frac{2 e^{2 x}-6 e^{-x}+9}{2+9 e^{-2 x}}\).
If C passes through the points
\(\left(0, \frac{1}{2}+\frac{\pi}{2 \sqrt{2}}\right) \text { and }\left(\alpha, \frac{1}{2} e^{2 \alpha}\right)\) then eα is equal to
1
\(\frac{3+\sqrt{2}}{3-\sqrt{2}}\)
2
\(\frac{3}{\sqrt{2}}\left(\frac{3+\sqrt{2}}{3-\sqrt{2}}\right)\)
3
\(\frac{1}{\sqrt{2}}\left(\frac{\sqrt{2}+1}{\sqrt{2}-1}\right)\)
4
\(\frac{\sqrt{2}+1}{\sqrt{2}-1}\)