1. Understanding the Problem and Identifying Key Information

We are given an ellipse and the coordinates of the midpoint of one of its chords. Our goal is to determine a specific parameter $\alpha$ related to the length of this chord.

• Equation of the Ellipse: The given ellipse is $\frac{x^2}{9}+\frac{y^2}{4}=1$.
  • By comparing this to the standard form $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, we can identify the semi-major axis squared $a^2=9$ (so $a=3$) and the semi-minor axis squared $b^2=4$ (so $b=2$).