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Answer please! In an ellipse, the distance between its focii is 6 and minor axis is 8. Then its eccentricity is,

In an ellipse, the distance between its focii is 6 and minor axis is 8. Then its eccentricity is,

  • Option 1)

    3/5

  • Option 2)

    1/2

  • Option 3)

    4/5

  • Option 4)

    1/\sqrt{5}

 
Answers (1)
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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

 

 

Length of major axis -

2b

- wherein

b\rightarrow Semi minor axis

 

 

Eccentricity -

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

- wherein

For the ellipse  

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

Distance between its focii is 6.

 2ae = 6; ae = 3

minor axis, 2b = 8; b=4

b2 = a2(1-e2)

b2 = a2- a2e2

a2=25 \Rightarrow a=5

 e=\sqrt{1-\frac{b^{2}}{a^{2}}}=\frac{3}{5}


Option 1)

3/5

this is correct option

Option 2)

1/2

this is incorrect option

Option 3)

4/5

this is incorrect option

Option 4)

1/\sqrt{5}

this is incorrect option

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