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  • The combined equation of the asymptotes of the hyperbola <img alt="\mathrm{2 x^2+5 x y+2 y^2-11 x-7 y=4=0 \text {, is }}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B

The combined equation of the asymptotes of the hyperbola

\mathrm{2 x^2+5 x y+2 y^2-11 x-7 y=4=0 \text {, is }}

\mathrm{2 x^2+5 x y+2 y^2-11 x-7 y+\lambda=0, \text { where } \lambda=}

Option: 1

-5


Option: 2

5


Option: 3

4


Option: 4

0


Answers (1)

best_answer

For the hyperbola

\mathrm{ S \equiv 2 x^2+5 x y+2 y^2-11 x-7 y-4=0, }            .......(1)
the combined equation of the asymptotes is

\mathrm{ 2 x^2+5 x y+2 y^2-11 x-7 y+\lambda=0 }

The centre of hyperbola (1) is obtained by solving

\mathrm{ \frac{\partial S}{\partial x} \equiv 4 x+5 y-11=0 }

And  \mathrm{\frac{\partial S}{\partial y}=5 x+4 y-7=0}

\therefore \quad  Centre is \mathrm{C(-1,3).}

As asymptotes pass through the centre, the condition is

\mathrm{ 2-15+18+11-21+\lambda=0 }

Or  \mathrm{ \begin{aligned} 31-36+\lambda & =0 \\ \lambda & =5 \end{aligned} }

The required equation of asymptotes is

\mathrm{ 2 x^2+5 x y+2 y^2-11 x-7 y+5=0 }
The answer is (b)

Posted by

HARSH KANKARIA

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