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

Question

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

Tardigrade Admin · Accepted Answer

Given, major axis =3 (minor axis) ⇒ 2 a=3(2 b) ⇒ a2=9 b2=9 a2(1-e2) ⇒ e=(2 √2/3)

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

$\frac{1}{3}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{2 2}{3}$

Given, major axis $= 3$ (minor axis)
$\Rightarrow 2 a = 3 (2 b)$
$\Rightarrow a^{2} = 9 b^{2} = 9 a^{2} (1 - e^{2})$
$\Rightarrow e = \frac{2 2}{3}$

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

31​

3​1​

2​1​

322​​

Given, major axis =3 (minor axis) ⇒2a=3(2b) ⇒a2=9b2=9a2(1−e2) ⇒e=322​​

$\frac{1}{3}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{2 2}{3}$

Given, major axis $= 3$ (minor axis)
$\Rightarrow 2 a = 3 (2 b)$
$\Rightarrow a^{2} = 9 b^{2} = 9 a^{2} (1 - e^{2})$
$\Rightarrow e = \frac{2 2}{3}$