it is known that the equation of hyperbola and that of its pair of asymptotes differ by constant . If equation of hyperbola is `x^(2) +4xy+3y^(2) -4x+2y+1=0` then find the equation of its pair of asymptoes.

Answer

`x^(2) +4xy+3y^(2)-4x+2y-21=0`

Explanation

Let te equation of pair of asymptotes be
`x^(2) +4xy+3y^(2)-4x+2y+1+k=0`
This is the equation of pair of straight lines
`:. |{:(1,,2,,-2),(2,,3,,1),(-2,,1,,1+k):}|=0`
`rArr 1(3+3k-1)-2(2+2k+2)-2(2+6)=0`
`rArr 3k+2-4k-8-16=0`
`rArr k=-22`