If the length of the major axis of the ellipse x 2 a 2 + y 2 b 2 = 1 is three times the length of minor axis, its eccentricity is

We have x 2 a 2 + y 2 b 2 = 1 Given, Length of the major axis = 3 Length of the minor axis ⇒ 2 a = 3 2 b ⇒ a = 3 b Now, e = 1 - b 2 a 2 ⇒ e = 1 - b 2 9 b 2 ⇒ e = 1 - 1 9 = 8 3 = 2 2 3

Mathematics - Ellipse Question with Solution | TestHub

MathematicsEllipseGeneralEasy2 minPYQ_2019

MathematicsEasysingle choice

If the length of the major axis of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is three times the length of minor axis, its eccentricity is

Options:

Answer:

Solution:

We have

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

Given,

$Length of the major axis = 3 (Length of the minor axis)$

$\Rightarrow (2 a) = 3 (2 b)$

$\Rightarrow a = 3 b$

Now,

$e = \sqrt{1 - \frac{b^{2}}{a^{2}}}$

$\Rightarrow e = \sqrt{1 - \frac{b^{2}}{9 b^{2}}}$

$\Rightarrow e = \sqrt{1 - \frac{1}{9}} = \frac{\sqrt{8}}{3} = \frac{2 \sqrt{2}}{3}$

Stream:BITSATSubject:MathematicsTopic:EllipseSubtopic:General

⏱ 2mℹ️ Source: PYQ_2019

Doubts & Discussion

Loading discussions...