The combined equation of the asymptotes of the hyperbola `2x^(2)+5xy+2y^(2)+4x+5y=0` is

Options

A. `2x^(2)+5xy+2y^(2)+4x+5y+2=0`
B. `2x^(2)+5xy+2y^(2)+4x+5y-2=0`
C. `2x^(2)+5xy+2y^(2)=0`
D. none of these

Explanation

Let the equation of asymptotes be
`2x^(2)+5xy+2y^(2)+4x+5y+lambda=0`……`(i)`
This equation represents a pair of straight lines. Therefore,
`abc+2fgh-af^(2)-bg^(2)-ch^(2)=0`
Here, `a=2`, `b=2`, `h=5//2`, `g=2`, `f=5//2` and `c=lambda`
`:.4lambda+25-(25)/(2)-8-(25)/(4)lambda=0implies-(9lambda)/(4)+(9)/(2)=0implieslambda=2`
Putting the value of `lambda` in `(i)`, we get
`2x^(2)+5xy+2y^(2)+4x+5y+2=0`
This is the equation of the asymptotes.