Question
If the line x+2 y=1, where R , does not meet the hyperbola x^ 2 -9 y^ 2 =9, then a possible value of is:
JEE Main
Mathematics
Hyperbola
2026
JEE Main 2026 (22 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 0.5
- B. 0.6
- C. 0.7
- D. 0.8
Answer
D. 0.8
Step-by-step solution
Hyperbola: x^2 9 - y^2 = 1. Line: y = 1 - x 2 . Substituting: x^2 - 9 (1- x)^2 4 = 9 (4 - 9 ^2)x^2 + 18 x - 45 = 0. For no intersection (when 4 - 9 ^2 0): discriminant D = 324 ^2 + 180(4 - 9 ^2) -1296 ^2 + 720 5 9 . | | > 5 3 0.745. Among the options, only = 0.8 satisfies this condition.
Related: Mathematics — Hyperbola · All PYQ Banks