Question

Find the eccentricity of the hyperbola whose latus rectum is half of its transverse axis.​

Answer 1

✔ Solution :-

Let the equation of hyperbola be [(x² / a²) - (y² / b²)] = 1

Then transverse axis = 2a and latus - rectum = (2b² / a)

According to question (2b² / a) = (1/2) × 2a

⇒ 2b² = a² (Since, b² = a² (e² − 1))

⇒ 2a² (e² − 1) = a²

⇒ 2e² – 2 = 1

⇒ e² = (3 / 2)

∴ e = √(3/2)

Hence,

• The required eccentricity is √(3/2)