HyperbolaHard
Question
The asymptotes of the hyperbola xy - 3x - 2y = 0 are -
Options
A.x - 2 = 0 and y - 3 = 0
B.x - 3 = 0 and y - 2 = 0
C.x + 2 = 0 and y + 3 = 0
D.x + 3 = 0 and y + 2 = 0
Solution
Let equation of asymptotes be xy - 3x - 2y + λ = 0.
Then abc + 2fgh - af2 - bg2 - ch2 = 0
⇒
= 0 ⇒ λ = 6
∴ Equation of asymptotes is xy - 3x - 2y + 6 = 0
i.e., (x - 2) (y - 3) = 0.
Then abc + 2fgh - af2 - bg2 - ch2 = 0
⇒
= 0 ⇒ λ = 6∴ Equation of asymptotes is xy - 3x - 2y + 6 = 0
i.e., (x - 2) (y - 3) = 0.
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