If \( \alpha x+\beta y=109 \) is the equation of the chord of the ellipse \(\displaystyle \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 \), whose mid point is \(\displaystyle \left(\frac{5}{2},\frac{1}{2}\right) \), then \( \alpha+\beta \) is equal to:
\( 72 \)
\( 58 \)
\( 46 \)
\( 37 \)
