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The center of a rectangular hyperbola li...

The center of a rectangular hyperbola lies on the line `y=2xdot` If one of the asymptotes is `x+y+c=0` , then the other asymptote is: (a) `6x+3y-4c=0` (b) `3x+6y-5c=0` (c) `3x-6y-c=0` (d) none of these

A

`6x+3y-4c=0`

B

`3x+6y-5c=0`

C

`3x-6y-c=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
The asymptotes of a rectangular hyperbola are perpendicular to each other.
Given one asymptote
`x+y+c=0`
Let the other asymptote be
`x-y+lambda=0`
We also know that the asymptotes pass through the centre of the hyperbola. Therefore, the line `2x-y=0` and the asymptotes must be concurrent.
Thus, we have
`|(2,-1,0),(1,1,c),(1,-1,lambda)|=0`
`"or "lambda=-(c)/(3)`
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