If the equation to the hyperbola is $5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y + 29 = 0$ and the equation of pair of asymptotes is $5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y + \frac{266}{11} = 0$ then the equation of conjugate hyperbola is

5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y - \frac{213}{11} = 0

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

5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y + 58 = 0

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

5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y + \frac{106}{11} = 0

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

5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y + \frac{213}{11} = 0

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

Open in App

Solution

The correct option is D $5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y + \frac{213}{11} = 0$
Given: Hyperbola $5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y + 29 = 0$ ; Pair of asymptotes $5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y + \frac{266}{11} = 0$

To Find: Equation of conjugate hyperbola

We know that, on adding the equation of a hyperbola and its conjugate hyperbola results into twice the equation of pair of asymptotes.

$∴ 5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y + 29 + (Conjugate hyperbola) = 2 (5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y + \frac{266}{11})$

$\Rightarrow Conjugate hyperbola = 5 x^{2} - 12 x y + 5 y^{2} + 22 x - 26 y + \frac{213}{11}$

Suggest Corrections

Similar questions

5 x^{2} - 6 x y + 5 y^{2} + 22 x - 26 y + 29 = 0

5 x^{2} + 12 x y - 22 x - 12 y - 19 = 0

19 x^{2} + 24 x y + y^{2} - 22 x - 6 y = 0 .

3 x^{2} - 5 x y - 2 y^{2} + 5 x + 11 y - 8 = 0

Join BYJU'S Learning Program