Question

The hyperbola$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ passes through the point ( $\sqrt{6 }$,3) and the length of the latus rectum is 18/5. Then the length of the transverse axis is equal to

• A. 5
• B. 4
• C. 3
• D. 2
• E. 1

Answer 1

Answer: (D)

Given, equation of hyperbola
$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \,...(i)$
Eq. (i) passes through $(\sqrt{6,3})$,
$\therefore \frac{(\sqrt{6})^{2}}{a^{2}}-\frac{(3)^{2}}{b^{2}}=1 \Rightarrow \frac{6}{a^{2}}-\frac{9}{b^{2}}=1 \,...(ii) $.
and $\frac{2 b^{2}}{a}=\frac{18}{5} \,.....(ii)$
On solving Eqs.(i) and (ii), we get
$a^{2}=1, b^{2}=\frac{9}{5}$
$\therefore $ Length of transverse axis is $=2 a$
$=2 \times 1=2$