The equation of the pair of asymptotes of the hyperbol $4 x^2-9 y^2-24 x-36 y-36=0$ is

The equation of the pair of asymptotes of the hyperbol $4 x^2-9 y^2-24 x-36 y-36=0$ is
  1. $2 x^2-x y-3 y^2-14 x-9 y-12=0$
  2. $2 x^2-x y-3 y^2-2 x+3 y=0$
  3. $2 x^2-5 x y+3 y^2-22 x-27 y+60=0$
  4. $4 x^2-9 y^2-24 x-36 y=0$

Solution

$\begin{aligned} & \text { } 4 x^2-9 y^2-24 x-36 y-36=0 \\ & \Rightarrow(2 x-6)^2-(3 y+6)^2=36 \\ & \Rightarrow \frac{(x-3)^2}{9}-\frac{(y+2)^2}{4}=1 \end{aligned}$
Equation of asymptotes $\frac{(x-3)^2}{9}-\frac{(y+2)^2}{4}=0$ $\Rightarrow 4 x^2-9 y^2-24 x-36 y=0$

Asked in: AP EAMCET 2024 (21 May Shift 1)

Practice more Hyperbola questions on Aicharya