Question

Find the asymptotes of curve x³+2x²y-xy²-2y³+x²-y²-2x-3y=0​

Answer 1

Step-by-step explanation:

Since equation of a hyperbola and its asymptotes differ in constant terms only,

∴ Pair of asymptotes is given by xy−3y−2x+λ=0

where λ is any constant such that it represents two straight lines.

∴abc+2fgh−af

2

−bg

2

−ch

2

=0⇒0+2×−

2

3

×−1

2

1

−0−0−λ(

2

1

)

2

=0∴λ=6

From (1) , the asymptotes of given hyperbola are given by

xy−3y−2x+6=0or(y−2)(x−3)=0∴ Asymptotes are x−3=0 and y−2=0

Was this answer helpfue