If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :-

Question

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :- (A) 2 (B) (13/6) (C) (13/8) (D) (13/12)

Tardigrade Admin · Accepted Answer

2b = 5 and 2ae = 13 b2 =a2 (e2 -1) ⇒ (25/4) = (169/4) -a2 ⇒ a =6 ⇒ e = (13/12)

Q. If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :-

2

$\frac{13}{6}$

$\frac{13}{8}$

$\frac{13}{12}$

$2 b = 5$ and $2 a e = 13$
$b^{2} = a^{2} (e^{2} - 1) \Rightarrow \frac{25}{4} = \frac{169}{4} - a^{2}$
$\Rightarrow a = 6 \Rightarrow e = \frac{13}{12}$

Q. If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :-

2

613​

813​

1213​

2b=5 and 2ae=13 b2=a2(e2−1)⇒425​=4169​−a2 ⇒a=6⇒e=1213​

$\frac{13}{6}$

$\frac{13}{8}$

$\frac{13}{12}$

$2 b = 5$ and $2 a e = 13$
$b^{2} = a^{2} (e^{2} - 1) \Rightarrow \frac{25}{4} = \frac{169}{4} - a^{2}$
$\Rightarrow a = 6 \Rightarrow e = \frac{13}{12}$