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

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) 3x2-y2=3 (B) x2-3y2=3 (C) 3x2-y2=9 (D) x2-3y2=9

Tardigrade Admin · Accepted Answer

According to given condition, 2 a e=2 ⋅ 2 a ⇒ e=2 and 2 b=6 ⇒ b=3 Hence, a=(3/√3)=√3 ∴ Required equation is (x2/3)-(y2/9)=1 ⇒ 3 x2-y2=9

Q. 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

$3 x^{2} - y^{2} = 3$

$x^{2} - 3 y^{2} = 3$

$3 x^{2} - y^{2} = 9$

$x^{2} - 3 y^{2} = 9$

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

Q. 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

3x2−y2=3

x2−3y2=3

3x2−y2=9

x2−3y2=9