Hyperbola
Hyperbola
nta_pyq_2025_jan
Grade 11
Question:
Let the foci of a hyperbola be (1, 14) and (1, -12). If it passes through the point (1, 6), then the length of its latus-rectum is :
24 5
25 6
144 5
288 5 2 2
Step-by-Step Solution
Key Concept: Apply the core result for hyperbola parameters and tangents and simplify using the given constraints.
(4) be = 13, b = 5 2 2 2 a = b (e - 1) 2 2 2 = b e - b = 169 - 25 = 144 2 2a 2 \times 144 288 ℓ( LR ) = = = b 5 5
Correct Answer: 4