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 $\frac{2b^2}{a}=\frac{18}{5}.....(ii)$
On solving Eqs.(i) and (ii), we get
$a^2=1,b^2=\frac{9}{5}$
$\therefore$ Length of transverse axis is $=2a$
$=2\times 1=2$