The equation of hyperbola conjugate to the hyperbola $2 x^{2} + 3 x y - 2 y^{2} - 5 + 5 y + 2 = 0$ is

2 x^{2} + 3 x y - 2 y^{2} - 5 x + 5 y - 8 = 0

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

x^{2} + 3 x y - 2 y^{2} - 5 x + 5 y + 8 = 0

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

2 x^{2} + 3 x y - 2 y^{2} + 5 x - 5 y - 8 = 0

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

None of these

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

Open in App

Solution

The correct option is A $2 x^{2} + 3 x y - 2 y^{2} - 5 x + 5 y - 8 = 0$
Let the given hyperbola be $H = 2 x^{2} + 3 x y - 2 y^{2} - 5 x + 5 y + 2 = 0$

Thus the pair of asymptotes be $A = 2 x^{2} + 3 x y - 2 y^{2} - 5 x + 5 y + λ = 0$

Pair of straight line has $Δ = 0$
$Δ = a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0$

where,
$a = 2$
$b = - 2$
$c = λ$
$f = \frac{5}{2}$
$g = - \frac{5}{2}$
$h = \frac{3}{2}$

Thus, $λ = - 3$

$A = 2 x^{2} + 3 x y - 2 y^{2} - 5 x + 5 y - 3 = 0$

Since $H + C = 2 A$ Where $C$ be the equation of conjugate hyperbola

$C = 2 A - H$
So,the equation of conjugate hyperbola be $C = 2 x^{2} + 3 x y - 2 y^{2} - 5 x + 5 y - 8 = 0$

Suggest Corrections

Similar questions

2 x^{2} + 3 x y - 2 y^{2} - 5 x + 5 y + 2 = 0

2 x^{2} + 3 x y - 2 y^{2} + 10 x + 5 y + 12 = 0

The equation of a hyperbola , conjugate to the hyperbola $x^{2} + 3 x y + 2 y^{2} + 2 x + 3 y = 0 i s$

2 x^{2} - 3 x y - 2 y^{2} + 3 x - y + 8 = 0

2 x^{2} + 3 x y - 2 y^{2} + 5 x - 5 y + 3 = 0

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

a + b = 0

Join BYJU'S Learning Program