Mathematics | VITEEE 2018 | Discussion Page

The combined equation of the asymptotes olthe hyperbola 2x² + 5xy + 2y² + 4x + 5y = 0 is -

A) $2x^{2} + 5xy + 2y^{2} + 4x + 5y+2 = 0$

B) $2x^{2} + 5xy + 2y^{2} + 4x + 5y-2 = 0$

C) $2x^{2} + 5xy + 2y^{2} = 0$

D) None of these

Option A

Let the equation of asymptotes be

2x² + 5xy + 2y² + 4x + 5y + λ = 0 ....(1)

This equation represents a pair of straight lines,

.'. abc + 2fgh - af² - bg² - ch² = 0

$\therefore 4\lambda+25-\frac{25}{2}-8-\lambda\times\frac{25}{4}=0$

$\Rightarrow -\frac{9\lambda}{4}+\frac{9}{2}=0$ $\Rightarrow \lambda=2$

Putting the value of λ, in eq. (1), we get

$2x^{2} + 5xy + 2y^{2} + 4x + 5y+2 = 0$

this is the equation of the asymptotes.

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