Find the asymptotes of the curve `x y-3y-2x=0` .

Answer

`x-3=0 and y-2=0`

Explanation

Since the equation of a hyperbola and its asymptotes differ in constant terms only, the pair of asymptotes is given by
`xy-3y-2x+lambda=0" (1)"`
where `lambda` is any constant such that it represents two straight lines.
Hence,
`abc+2fgh-af^(2)-bg^(2)-ch^(2)=0`
`"or "0+2xx(-(3)/(2))xx(-1)xx((1)/(2))-0-0-lamda((1)/(2))^(2)=0`
`"or "lambda=6`
From (1), the asymptotes of the given hyperbola are given by
`xy-3y-2x+6=0`
`" "(y-2)(x-3)=0`
Therefore, the asymptotes are `x-3=0 and y-2=0.`