Angle between asymptotes of hyperbola xy=8 is

Solution :

Since given hyperbola xy = 8 is rectangular hyperbola.

And eccentricity of rectangular hyperbola is \(\sqrt{2}\)

Angle between asymptotes of hyperbola is \(2sec^{-1}(e)\)

\(\implies\) \(\theta\) = \(2sec^{-1}(\sqrt{2})\)

\(\implies\) \(\theta\) = \(2sec^{-1}(sec 45)\)

\(\implies\) \(\theta\) = 2(45) = 90

---

Similar Questions

Find the normal to the hyperbola \(x^2\over 16\) – \(y^2\over 9\) = 1 whose slope is 1.

Find the asymptotes of the hyperbola \(2x^2 + 5xy + 2y^2 + 4x + 5y\) = 0. Find also the general equation of all the hyperbolas having the same set of asymptotes.

Find the equation of the tangent to the hyperbola \(x^2 – 4y^2\) = 36 which is perpendicular to the line x – y + 4 = 0

The eccentricity of the conjugate hyperbola to the hyperbola \(x^2-3y^2\) = 1 is

If the foci of a hyperbola are foci of the ellipse \(x^2\over 25\) + \(y^2\over 9\) = 1. If the eccentricity of the hyperbola be 2, then its equation is :