Q94 / 180 · KCET 2011 · Mathematics
The equation of a hyperbola whose asymptotes are $3 x \pm 5 y=0$ and vertices are $(\pm 5,0)$ is
- A$3 x^{2}-5 y^{2}=25$
- B$5 x^{2}-3 y^{2}=225$
- C$25 x^{2}-9 y^{2}=225$
- Correct answerD$9 x^{2}-25 y^{2}=225$
Solution
The given equation of asymptotes of hyperbola is
$\begin{array}{cc}3 x \pm 5 y=0 \\ \text { and vertices } & (\pm 5,0)\end{array}$
Now, equation of hyperbola is
$$
\begin{gathered}
(3 x+5 y)(3 x-5 y)=\lambda \\
9 x^{2}-25 y^{2}=\lambda
\end{gathered}
$$
Since, $(\pm 5,0)$ is the vertices of the hyperbola, then
$$
9(5)^{2}-0=\lambda \Rightarrow \lambda=225
$$
From Eq. (ii), $9 x^{2}-25 y^{2}=225$
Hence, the correct answer is option: 'D'.