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  • I need help with Let the length of the latur rectum of an ellipse with its major axis along x-axis and center at the origin be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following po

Let the length of the latur rectum of an ellipse with its major axis along x-axis and center at the origin be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it ?

  • Option 1)

    (4\sqrt3,2\sqrt2)

  • Option 2)

    (4\sqrt2,2\sqrt2)

  • Option 3)

    (4\sqrt3,2\sqrt3)

     

  • Option 4)

    (4\sqrt2,2\sqrt3)

Answers (1)

best_answer

 

Sum of focal distance -

2a

- wherein

 

 

Length of latus rectum of ellipse -

\frac{2b^{2}}{a}

- wherein

For the ellipse  

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

Latus rectum, \frac{2b^{2}}{a}=8

and

2ae=2b

=>e=\frac{b}{a}

=>1-e^{2}=e^{2}

=>e=\frac{1}{\sqrt2}

=>b=4{\sqrt2}    and   a=8

So, equation of ellipse is  \frac{x^{2}}{64}+\frac{y^{2}}{32}=1

 

 


Option 1)

(4\sqrt3,2\sqrt2)

Option 2)

(4\sqrt2,2\sqrt2)

Option 3)

(4\sqrt3,2\sqrt3)

 

Option 4)

(4\sqrt2,2\sqrt3)

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