If αx + β y = 109 is the equation of the chord of the ellipse 9 x 2 + 4 y 2 = 1 , whose mid point is ( 2 5 , 2 1 ) , then α + β is equal to :

Question

If αx + β y = 109 is the equation of the chord of the ellipse 9 x 2 ​ + 4 y 2 ​ = 1 , whose mid point is ( 2 5 ​ , 2 1 ​ ) , then α + β is equal to :

TestHub · Accepted Answer

Equation of chord T = S 1 ​ ​ 2 5 ​ ( 9 x ​ ) + 2 1 ​ ( 4 y ​ ) = 36 25 ​ + 16 1 ​ ⇒ 18 5 x ​ + 8 y ​ = 144 100 + 9 ​ = 144 109 ​ ⇒ 40 x + 18 y = 109 ⇒ α = 40 , β = 18 ⇒ α + β = 58 ​

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