Ellipse
Ellipse
nta_pyq_2025_jan
Grade 11
Question:
If \alphax + \betay = 109 is the equation of the chord of the ellipse 2 y , whose mid point is ( , then \alpha + \beta x 5 1 + = 1 , ) 9 4 2 2 is equal to :
Step-by-Step Solution
Key Concept: Apply the core result for ellipse parameters and tangents and simplify using the given constraints.
(1) Equation of chord T = S 1 5 x 1 y 25 1 ( ) + ( ) = + 2 9 2 4 36 16 5x y 100 + 9 109 \Rightarrow + = = 18 8 144 144 \Rightarrow 40x + 18y = 109 \Rightarrow \alpha = 40, \beta = 18 \Rightarrow \alpha + \beta = 58
Correct Answer: 1