Question

Find the asymptotes of the hyperbola xy - 3y - 2x = 0

• A. x = 3
• B. x = 2
• C. y = 2
• D. y = 3

Answer 1

Answer: (A), (C)

y = 2

Equation of hyperbola and the equation of aysmptotes differ in constant part only.

$\therefore$ pair of aymptotes is given by

$xy-3y-2x+\lambda =0$

Where $\lambda$ is any constant such that it represents two straight lines

If $a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$ represents a pair of straight lines then

$abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0$

$\Rightarrow 0+2\times \left(\frac{-3}{2}\right)\times (-1)\times \frac{1}{2}-0-0-\lambda {\left(\frac{1}{2}\right)}^2=0$

$\frac{3}{2}-\frac{\lambda }{4}=0$

$\therefore \lambda =6$

pair of asymptotes of the given hyperbola is

xy-3y-2x+6=0

or

(y-2)(x-3)=0

Asymptotes are x-3=0 and y-2=0