If α x+β y=109 is the equation of the chord of the ellipse (x²)/9+(y²)/4=1, whose midpoint is (5/2, 1/2), then α+β is equal to:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q138

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumCoordinate Geometry478× since 2002

\alpha x+\beta y=109

is the equation of the chord of the ellipse

\frac{x^2}{9}+\frac{y^2}{4}=1

, whose midpoint is

\left(\frac{5}{2}, \frac{1}{2}\right)

, then

\alpha+\beta

is equal to: