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 `6x+3y-4c=0` (b) `3x+6y-5c=0` `3x-6y-c=0` (d) none of these

Options

A. `6x+3y-4c=0`
B. `3x+6y-5c=0`
C. `3x-6y-c=0`
D. none of these

Answer

D

Explanation

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)`