Question

The equation of the hyperbola whose conjugate axis is $5$ and the distance between the foci is $13$ , is

• A. $25 x^{2}-144 y^{2}=900$
• B. $144 x^{2}-25 y^{2}=900$
• C. $144 x^{2}+25 y^{2}=900$
• D. $25 x^{2}+144 y^{2}=900$

Answer 1

Answer: (A)

Conjugate axis is $5$ and distance between foci $=13$
$\Rightarrow 2 b =5$ and $2 ae =13$
Now, also we know for hyperbola
$b^{2}=a^{2}\left(c^{2}-1\right) \Rightarrow \frac{25}{4}=\frac{(13)^{2}}{4 e^{2}}\left(e^{2}-1\right)$
$\Rightarrow \frac{25}{4}=\frac{169}{4}-\frac{169}{4 e ^{2}}$ or $e ^{2}=\frac{169}{144} \Rightarrow e =\frac{13}{12}$
or $a=6, b=\frac{5}{2}$ or hyperbola is $\frac{x^{2}}{36}-\frac{y^{2}}{\frac{25}{4}}=1$
$\Rightarrow 25 x^{2}-144 y^{2}=900$