Question

For a hyperbola whose centre is at $(1,2)$ and asymptotes are parallel to line $2x+3y=0$ and $x+2y=1$, then equation of hyperbola passing through $(2,4)$ is :

• A. $(2x+3y-5)(x+2y-8)=40$
• B. $(2x+3y-8)(x+2y-5)=40$
• C. $(2x+3y-8)(x+2y-5)=30$
• D. None of these

Answer 1

Answer: (B)

$(2x+3y-8)(x+2y-5)=40$

Let the asymptotes be $2x+3y+{\lambda }_1=0$ and $x+2y+{\lambda }_2=0$
Since, asymptotes will pass through centre $(1,2).$
$\Rightarrow {\lambda }_1=-8,{\lambda }_2=-5$
The equation of the hyperbola is
$(2x+3y-8)(x+2y-5)+\lambda =0$
Since, it passes through $(2,4).$
$\Rightarrow \lambda =-40$
Hence, equation of hyperbola is
$(2x+3y-8)(x+2y-5)=40$