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  • The centre of a rectangular hyperbola lies on the line y=2x. If one of the asymptotes is  <img alt="\mathrm{x+y+c=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmat

The centre of a rectangular hyperbola lies on the line y=2x. If

one of the asymptotes is  \mathrm{x+y+c=0}, then the other asymptote 

is

Option: 1

\mathrm{6 x+3 y-4 c=0}


Option: 2

\mathrm{3 x+6 y-5 c=0}


Option: 3

\mathrm{3 x-6 y-5 c=0}


Option: 4

None of these


Answers (1)

best_answer

The asymptotes of a rectangular hyperbola are

perpendicular to each other.

Given one asymptote

      \mathrm{x+y+c=0}

Let the other asymptote be

       \mathrm{x-y+\lambda=0}

We also know that the asymptotes pass through the centre

of the hyperbola. Therefore, the line  \mathrm{2x-y=0}  and the

asymptotes must be concurrent.

Thus, we have

\mathrm{\begin{aligned} & \left|\begin{array}{ccc} 2 & -1 & 0 \\ 1 & 1 & c \\ 1 & -1 & \lambda \end{array}\right|=0 \\ & \text { or } \lambda=-\frac{c}{3} \end{aligned}}

 

 

Posted by

seema garhwal

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