An ellipse has OB as semi minor axis, F\; and\; F'  its focii and the angle FB F'  is a right angle. Then the eccentricity of the ellipse is

  • Option 1)

    \frac{1}{2}\;

  • Option 2)

    \; \frac{1}{\sqrt{2}}\;

  • Option 3)

    \; \frac{1}{\sqrt{3}}\;

  • Option 4)

    \; \frac{1}{4}\;

 

Answers (1)

As we learnt in 

Coordinates of foci -

\pm ae,o

- wherein

For the ellipse  

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

 

 and

Length of major axis -

2b

- wherein

b\rightarrow Semi minor axis

 \angle OBF_{2}=45^{0}

so, OB = OF2

i.e b = ae

also b2 = a2(1 - e2)

a2e2 = a2(1 - e2)

e2=1/2 

\Rightarrow e=\frac{1}{\sqrt{2}}


Option 1)

\frac{1}{2}\;

this is incorrect

Option 2)

\; \frac{1}{\sqrt{2}}\;

this is correct

Option 3)

\; \frac{1}{\sqrt{3}}\;

this is incorrect

Option 4)

\; \frac{1}{4}\;

this is incorrect

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