Ellipse
Ellipse
nta_pyq_2025_jan
Grade 11
Question:
The length of the chord of the ellipse 2 y , whose mid-point is (1, , is : x 1 + = 1 ) 4 2 2
5 3 \sqrt15
1 3 \sqrt15
2 3 \sqrt15
\sqrt15 2
Step-by-Step Solution
Key Concept: Apply the core result for ellipse parameters and tangents and simplify using the given constraints.
T = S1 x ⋅ 1 y 1 1 (3) + = + 4 4 4 8 \Rightarrow 2x + 2y = 3 2 3-2x 2 ( ) x 2 + = 1 4 2 12 $\pm$ \sqrt120 1 \sqrt120 \Rightarrow x = \Rightarrow y = ∓ 12 2 12 So length of chord 2\sqrt15 = 3
Correct Answer: 3