CON011 · Conic sections · Classes 11–12
Hyperbola eccentricity
For a hyperbola x²/a² − y²/b² = 1, c² = a² + b² and the eccentricity e = c/a is always greater than 1.
e > 1Hyperbola eccentricity
📐 Formula
e = c/a = √(1 + b²/a²)
✏️ Worked example
a = 3, b = 4: c = 5, e = 5/3 ≈ 1.67; asymptotes y = ±(4/3)x.
🌍 Where it is used
Navigation systems (LORAN) and some comet paths.
❓ Quick check
Eccentricity of a rectangular hyperbola (a = b)?
🏋️ Practice
Easya = 6, b = 8. e?
Answer: 5/3
MediumAsymptotes of x²/9 − y²/16 = 1?
Answer: y = ±4x/3
ChallengeCan a hyperbola have e = 0.9?
Answer: No