The separate equations of the asymptotes of rectangular hyperbola $x^{2} + 2 x y cot 2 α - y^{2} = a^{2}$ are :

x cot α - y = 0, x tan α + y = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x cot α + y = 0, x tan α + y = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x cot α + y = 0, x tan α - y = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x cot α - y = 0, x tan α - y = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $x cot α - y = 0, x tan α + y = 0$
Given, $x^{2} + 2 x y cot 2 α - y^{2} = a^{2}$
$\Rightarrow x^{2} + \frac{2 x y (1 - {tan}^{2} α)}{2 tan α} - y^{2} = a^{2}$
$\Rightarrow x^{2} + x y (cot α - tan α) - y^{2} = a^{2}$

For asymptotes
$x^{2} + x y (cot α - tan α) - y^{2} + λ = 0$

this will be a pair for st. line if
$Δ = 0 \Rightarrow λ = 0$
$\Rightarrow x (x + y cot α) - y tan α (x + y cot α) = 0 \Rightarrow (x - y tan α) (x + y cot α) = 0$

$∴$ separate equation asymptotes are
$x + y cot α = 0; x - y tan α = 0$

Suggest Corrections

Similar questions

Q. The separate equations of the asymptotes of rectangular hyperbola

x^{2} + 2 x y cot 2 α - y^{2} = a^{2}

are :

Which of the following statements are correct?

1. The particular kind of hyperbola in which the lengths of the transverse and conjugate axis are equal is called an equilateral hyperbola.

2. Eccentricity of equilateral hyperbola = $\sqrt{2}$
3. Equation of pair of asymptotes of rectangular hyperbola $x^{2} - y^{2} = a^{2}$ is $x^{2} - y^{2} = 0$

4. Equation of pair of asymptotes of rectangular hyperbola $x^{2} - y^{2} = a^{2}$ is $x^{2} - y^{2} = - a^{2}$

The combined equation of the asymptotes of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ is $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = - 1$ ..

Q. From any point on the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

tangents are drawn to the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 2

. The area cut-off by the chord of contact on the asymptotes is equal to

Q. From any point on the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

tangents are drawn to the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 2

. Then area cut-off by the chord of contact on the asymptotes is equal to :

Join BYJU'S Learning Program

The separate equations of the asymptotes of rectangular hyperbola x2+2xycot2α−y2=a2 are :

The separate equations of the asymptotes of rectangular hyperbola $x^{2} + 2 x y cot 2 α - y^{2} = a^{2}$ are :