Question

The asymptotes of the hyperbola $xy-3x+4y+2=0$

• A. $x=-4$
• B. $x=4$
• C. $y=-3$
• D. $y=3$

Answer 1

Answer: (A), (D)

The correct options are
A $x=-4$
D $y=3$

Since the equation of a hyperbola and its asymptotes differ in constant terms only. Therefore, the equations of asymptotes of the given hyperbola are given by $xy-3x+4y+k=0$

where $k$ is a constant to be determined by the condition that $abc+2fgh-{af}^2-{bg}^2-{ch}^2=0$

i.e., $0+2\times 2\times \left(\frac{-3}{2}\right)\times \frac{1}{2}-0-0-k\times {\left(\frac{1}{2}\right)}^2=0\Rightarrow k=-12$

$\because$ Asymptotes of the given hyperbola are $xy-3x+4y-12=0$ or $(x+4)(y-3)=0$

i.e., $x=-4$ and $y=3.$