Question

The distance between the foci of a hyperbola is double the distance between its vertices and the length of its conjugate axis is $6 .$ The equation of the hyperbola referred to its axes as axes of coordinates are

• A. $3x^{2}-y^{2}=3$
• B. $x^{2}-3y^{2}=3$
• C. $3x^{2}-y^{2}=9$
• D. $x^{2}-3y^{2}=9$

Answer 1

Answer: (C)

According to given condition, $2 a e=2 \cdot 2 a$
$\Rightarrow e=2$
and $2 b=6 \Rightarrow b=3$
Hence, $a=\frac{3}{\sqrt{3}}=\sqrt{3}$
$\therefore $ Required equation is
$\frac{x^{2}}{3}-\frac{y^{2}}{9}=1$
$\Rightarrow 3 x^{2}-y^{2}=9$