Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# The Eccentricity of the Ellipse, If the Minor Axis is Equal to the Distance Between the Foci, is - Mathematics

MCQ
Short Note
Sum

The eccentricity of the ellipse, if the minor axis is equal to the distance between the foci, is

#### Options

• $\frac{\sqrt{3}}{2}$

• $\frac{2}{\sqrt{3}}$

• $\frac{1}{\sqrt{2}}$

• $\frac{\sqrt{2}}{3}$

#### Solution

$\frac{1}{\sqrt{2}}$
According to the question, the minor axis is equal to the distance between the foci.
$i . e . 2b = 2ae$
$\Rightarrow e = \frac{b}{a} . . . (1)$
$\text{ Now,} e = \sqrt{1 - \frac{b^2}{a^2}}$
$\Rightarrow e = \sqrt{1 - e^2} [From (1)]$
On squaring both sides, we get:
$e^2 = 1 - e^2$
$\Rightarrow 2 e^2 = 1$
$\Rightarrow e^2 = \frac{1}{2}$
$\Rightarrow e = \frac{1}{\sqrt{2}}$

Concept: Introduction of Ellipse
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 26 Ellipse
Q 6 | Page 28