If the eccentricity of a hyperbola is √3, then the eccentricity of its conjugate hyperbola is

Question

If the eccentricity of a hyperbola is √3, then the eccentricity of its conjugate hyperbola is (A)  √2  (B)  √3  (C)  √(3/2)  (D)  2√3

Tardigrade Admin · Accepted Answer

Let e and e are the eccentricities of a hyperbola and its conjugate hyperbola. We know that, (1/e2)+(1/(e')2)=1 ⇒ (1/3)+(1/(e')2)=1 ⇒ (1/(e')2)=(2/3) ⇒ e '=√(3/2)

Q. If the eccentricity of a hyperbola is $3,$ then the eccentricity of its conjugate hyperbola is

$2$

$3$

$\frac{3}{2}$

$23$

Let e and e are the eccentricities of a hyperbola and its conjugate hyperbola.
We know that,
$\frac{1}{e ^{2}} + \frac{1}{( e ^{'} ) ^{2}} = 1$
$\Rightarrow \frac{1}{3} + \frac{1}{( e ^{'} ) ^{2}} = 1$
$\Rightarrow \frac{1}{( e ^{'} ) ^{2}} = \frac{2}{3}$
$\Rightarrow e^{'} = \frac{3}{2}$

Q. If the eccentricity of a hyperbola is 3​, then the eccentricity of its conjugate hyperbola is

2​

3​

23​​

23​

Let e and e are the eccentricities of a hyperbola and its conjugate hyperbola. We know that, e21​+(e′)21​=1 ⇒31​+(e′)21​=1 ⇒(e′)21​=32​ ⇒e′=23​​

Q. If the eccentricity of a hyperbola is $3,$ then the eccentricity of its conjugate hyperbola is

$2$

$3$

$\frac{3}{2}$

$23$

Let e and e are the eccentricities of a hyperbola and its conjugate hyperbola.
We know that,
$\frac{1}{e ^{2}} + \frac{1}{( e ^{'} ) ^{2}} = 1$
$\Rightarrow \frac{1}{3} + \frac{1}{( e ^{'} ) ^{2}} = 1$
$\Rightarrow \frac{1}{( e ^{'} ) ^{2}} = \frac{2}{3}$
$\Rightarrow e^{'} = \frac{3}{2}$