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
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).