Question

Let \(\dfrac32\) be the eccentricity of the conjugate hyperbola of a hyperbola \(H\) and one of the foci of \(H\) lie on the straight line \[ x+y-3=0. \] If the transverse and conjugate axes of \(H\) are along \(X\)-axis and \(Y\)-axis respectively, then the length of the latus rectum of \(H\) is

• A. \(\dfrac{4}{\sqrt5}\)
• B. \(\dfrac{8}{\sqrt5}\)
• C. \(\dfrac{10}{3}\)
• D. \(\dfrac53\)

Hint:

For the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1, \] \[ \boxed{c^2=a^2+b^2} \] and \[ \boxed{\text{Length of latus rectum}=\frac{2b^2}{a}.} \]

Answer 1

The Correct Option is B