If the length of major axis of an ellipse is three times the length of its minor axis, then its eccentricity is

Question

If the length of major axis of an ellipse is three times the length of its minor axis, then its eccentricity is (A)  (1/√3)  (B)  (2√2/3)  (C)  (1/√2)  (D)  (1/3)

Tardigrade Admin · Accepted Answer

Let major axis is o and minor axis is b. Given, a=3b ∴ Eccentricity, e=√1-(b2/a2) ⇒ e=√1-(b2/9b2) ⇒ 3=√(9-1/9) =(2√2/3)

Q. If the length of major axis of an ellipse is three times the length of its minor axis, then its eccentricity is

$\frac{1}{3}$

$\frac{2 2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

Let major axis is o and minor axis is b. Given,
$a = 3 b$ $∴$ Eccentricity, $e = 1 - \frac{b ^{2}}{a ^{2}}$
$\Rightarrow$ $e = 1 - \frac{b ^{2}}{9 b ^{2}}$
$\Rightarrow$ $3 = \frac{9 - 1}{9}$
$= \frac{2 2}{3}$

Q. If the length of major axis of an ellipse is three times the length of its minor axis, then its eccentricity is

3​1​

322​​

2​1​

31​

Let major axis is o and minor axis is b. Given, a=3b ∴ Eccentricity, e=1−a2b2​​ ⇒ e=1−9b2b2​​ ⇒ 3=99−1​​ =322​​

$\frac{1}{3}$

$\frac{2 2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

Let major axis is o and minor axis is b. Given,
$a = 3 b$ $∴$ Eccentricity, $e = 1 - \frac{b ^{2}}{a ^{2}}$
$\Rightarrow$ $e = 1 - \frac{b ^{2}}{9 b ^{2}}$
$\Rightarrow$ $3 = \frac{9 - 1}{9}$
$= \frac{2 2}{3}$