Q94 / 160 · AP EAMCET 2024 (21 May Shift 1) · Mathematics
The equation of the pair of asymptotes of the hyperbol $4 x^2-9 y^2-24 x-36 y-36=0$ is
- A$2 x^2-x y-3 y^2-14 x-9 y-12=0$
- B$2 x^2-x y-3 y^2-2 x+3 y=0$
- C$2 x^2-5 x y+3 y^2-22 x-27 y+60=0$
- Correct answerD$4 x^2-9 y^2-24 x-36 y=0$
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 $\frac{(x-3)^2}{9}-\frac{(y+2)^2}{4}=0$ $\Rightarrow 4 x^2-9 y^2-24 x-36 y=0$
Equation of asymptotes $\frac{(x-3)^2}{9}-\frac{(y+2)^2}{4}=0$ $\Rightarrow 4 x^2-9 y^2-24 x-36 y=0$
Hence, the correct answer is option: 'D'.