QJEEM25Ma9201: JEE Main 2025 Mathematics - Class 11 JEEM25Ma9201 Solution: If is the equation of the chord of the ellipse , whose mid…

$\begin{aligned}&\text { Equation of chord } \mathrm{T}=\mathrm{S}_1\\&\begin{aligned}& \frac{5}{2}\left(\frac{\mathrm{x}}{9}\right)+\frac{1}{2}\left(\frac{\mathrm{y}}{4}\right)=\frac{25}{36}+\frac{1}{16} \\& \Rightarrow \frac{5 \mathrm{x}}{18}+\frac{\mathrm{y}}{8}=\frac{100+9}{144}=\frac{109}{144} \\& \Rightarrow 40 \mathrm{x}+18 \mathrm{y}=109 \\& \Rightarrow \alpha=40, \beta=18 \\& \Rightarrow \alpha+\beta=58\end{aligned}\end{aligned}$