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  • The combined equation of the asymptotes of the hyperbola <img alt="\mathrm{2 x^2+5 x y+2 y^2+4 x+5 y=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B2%20x%5E2&plu

The combined equation of the asymptotes of the hyperbola

\mathrm{2 x^2+5 x y+2 y^2+4 x+5 y=0}  is

Option: 1

\mathrm{2 x^2+5 x y+2 y^2+4 x+5 y+2=0}


Option: 2

\mathrm{2 x^2+5 x y+2 y^2+4 x+5 y-2=0}


Option: 3

\mathrm{2 x^2+5 x y+2 y^2}


Option: 4

None of these


Answers (1)

best_answer

Let the equation of asymptotes be

\mathrm{2 x^2+5 x y+2 y^2+4 x+5 y+\lambda=0}                           ........(1)

This equation represents a pair of straight lines,Therefore,

\mathrm{a b c+2 f g h-a f^2-b g^2-c h^2=0}

Here,  \mathrm{a=2, b=2, h=5 / 2, g=2, f=5 / 2 \text { and } c=\lambda}

\mathrm{\therefore 4 \lambda+25-\frac{25}{2}-8-\frac{25}{4} \lambda=0 \Rightarrow-\frac{9 \lambda}{4}+\frac{9}{2}=0 \Rightarrow \lambda=2}

Putting the value \mathrm{\lambda} in (1), we get

\mathrm{2 x^2+5 x y+2 y^2+4 x+5 y+2=0}

This is the equation of the asymptotes. 

Posted by

Deependra Verma

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