Question

The given equation of rectangular hyperbola is \[ x^2 - y^2 = 6^2 \quad \text{(length of latus rectum is 16)} \] The asymptotes are parallel to each other

• A. \( x = \pm \sqrt{5} \)
• B. \( y = \pm \sqrt{5} \)
• C. \( x = \pm \sqrt{2} \)
• D. \( x = \pm \sqrt{3} \)

Hint:

For a rectangular hyperbola, the asymptotes are given by \( x = \pm \sqrt{a} \), where \( a \) is the constant in the equation \( x^2 - y^2 = a^2 \).

Answer 1

The Correct Option is A

The equation of the hyperbola \( x^2 - y^2 = a^2 \) represents a rectangular hyperbola, and the asymptotes of such a hyperbola are lines \( x = \pm \sqrt{a} \).