If the latus rectum subtends a right angle at the centre of the hyperbola x^2/a^2 - y^2/b^2 = 1,

Question

If the latus rectum subtends a right angle at the centre of the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) , then its eccentricity is

(a) \(\frac{\sqrt 5 + 1}{2}\)

(b) 3

(c) \(\frac{\sqrt 5 }{2}\)

(d) \(\sqrt\frac{ \sqrt 5 + 3}{2}\)

Answer 1

Correct option is (d) \(\sqrt\frac{ \sqrt 5 + 3}{2}\) 

[If \(e = \sqrt{\frac{3 - \sqrt 5}{2}} < 1\) but ecentricity of hyperbola > 1 so neglecting this value of e]