Question

# If distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is

A
12
B
23
C
13
D
45

Solution

## The correct option is B $$\displaystyle \frac{1}{\sqrt {3}}$$$$Distance\quad between\quad the\quad directrices\quad is\quad \dfrac { 2a }{ e }$$$$Distance\quad between\quad the\quad foci\quad is\quad 2ae$$$$Given\quad :\quad \dfrac { 2a }{ e } =3*2ae$$$$Or,\quad { e }^{ 2 }=\dfrac { 1 }{ 3 }$$$$\therefore \quad e=\dfrac { 1 }{ \sqrt { 3 } }$$Option [C]Mathematics

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