AP EAMCET · Maths · Hyperbola
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 \(2 x^2-5 x y+3 y^2-22 x-27 y+60=0\)
- D \(4 x^2-9 y^2-24 x-36 y=0\)
Answer & Solution
Correct Answer
(D) \(4 x^2-9 y^2-24 x-36 y=0\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } 4 x^2-9 y^2-24 x-36 y-36=0 \\ & \Rightarrow(2 x-6)^2-(3 y+6)^2=36 \\ & \Rightarrow \frac{(x-3)^2}{9}-\frac{(y+2)^2}{4}=1 \end{aligned}\) Equation of asymptotes \(\frac{(x-3)^2}{9}-\frac{(y+2)^2}{4}=0\) \(\Rightarrow 4 x^2-9 y^2-24 x-36 y=0\)
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