The length of the chord of the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{2}=1\), whose mid-point is \(\left(1, \frac{1}{2}\right)\), is:

1
\(\frac{2}{3} \sqrt{15}\)
2
\(\frac{5}{3} \sqrt{15}\)
3
\(\frac{1}{3} \sqrt{15}\)
4
\(\sqrt{15}\)

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