A hyperbola has its centre at the origin, passes through the point (4,2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :

Question

A hyperbola has its centre at the origin, passes through the point (4,2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is : (A) (2/√3) (B) (3/2) (C) √3 (D) 2

Tardigrade Admin · Accepted Answer

(x2/a2) - (y2/b2) = 1 2a =4 a=2 (x2/4) - (y2/b2) = 1 Passes through (4,2) 4 - (4/b2) = 1 ⇒ b2 = (4/3) ⇒ e = (2/√3)

Q. A hyperbola has its centre at the origin, passes through the point $(4, 2)$ and has transverse axis of length $4$ along the x-axis. Then the eccentricity of the hyperbola is :

$\frac{2}{3}$

$\frac{3}{2}$

$3$

$2$

$\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$
$2 a = 4 a = 2$
$\frac{x ^{2}}{4} - \frac{y ^{2}}{b ^{2}} = 1$
Passes through $(4, 2)$
$4 - \frac{4}{b ^{2}} = 1 \Rightarrow b^{2} = \frac{4}{3} \Rightarrow e = \frac{2}{3}$

Q. A hyperbola has its centre at the origin, passes through the point (4,2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :

3​2​

23​

3​

2

a2x2​−b2y2​=1 2a=4a=2 4x2​−b2y2​=1 Passes through (4,2) 4−b24​=1⇒b2=34​⇒e=3​2​

Q. A hyperbola has its centre at the origin, passes through the point $(4, 2)$ and has transverse axis of length $4$ along the x-axis. Then the eccentricity of the hyperbola is :

$\frac{2}{3}$

$\frac{3}{2}$

$3$

$2$

$\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$
$2 a = 4 a = 2$
$\frac{x ^{2}}{4} - \frac{y ^{2}}{b ^{2}} = 1$
Passes through $(4, 2)$
$4 - \frac{4}{b ^{2}} = 1 \Rightarrow b^{2} = \frac{4}{3} \Rightarrow e = \frac{2}{3}$