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JEE Main202529 Jan 2025Evening ShiftMathematicsEllipseActual

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

Options

A58
B46
C37
D72

Correct answer

A. 58

Step-by-step solution

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

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