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Question

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


A
12
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B
23
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C
13
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D
45
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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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