+2 votes
in JEE by kratos

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

1 Answer

+3 votes
by kratos
 
Best answer

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).

...