Given equation of hyperbola, is 2x2+5xy+2y2−11x−7y−4=0 The equation of pair of asymptotes, is 2x2+5xy+2y2−11x−7y+λ=0...(i) ∴‌‌abc+2fgh−af2−bg2−ch2=0
(2)(2)(λ)+2(‌
−7
2
)(‌
−11
2
)(‌
5
2
)−2(‌
−7
2
)2−2(‌
−11
2
)2−λ(‌
5
2
)2=0 4λ+‌
385
4
−2(‌
49
4
)−2(‌
121
4
)−λ(‌
25
4
)=0
16λ+385−98−242−25λ=0 45−9λ=0 ⇒‌‌λ=5 From Eq. (i) 2x2+5xy+2y2−11x−7y+5=0