Question

If angle between asymptote of hyperbola (x²/a²) – (y²/b²) = 1 is 45°. The value of eccentricity is ........

(a) √(4 ± 2√2)

(b) √(4 + 2√2)

(c) √(4 – 2√2)

(d) none of these

Answer 1

The correct option (c) √(4 – 2√2)

Explanation:

 2tan^–1(b/a) = 45

⇒   (b/a) = tan[22(1/2)]

∴  (b²/a²) = (√2 – 1)²

i.e.   [{a²(e² – 1)}/a²] = (√2 – 1)² 

∴   e² – 1 = 2 ÷ 2√2 + 1

∴    e² = 4 – 2√2

∴   e = √(4 – 2√2).