# In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is $10$ and one of the foci is at $\left ( 0,5\sqrt{3} \right )$, then the length of its latus rectum is : Option 1)$10$Option 2)$5$Option 3)$8$Option 4)$6$

P Plabita

focus is at  $\left ( 0,5\sqrt{3} \right )$

given difference of major axis-minor axis $=10$

$b-a=5$

$be=5\sqrt{3}$

$a^{2}=b^{2}\left ( 1-e^{2} \right )=b^{2}-\left ( be \right )^{2}$

$b=10,a=5$

Length of LR = $\frac{2a^{2}}{b}=5$

Option 1)

$10$

Option 2)

$5$

Option 3)

$8$

Option 4)

$6$

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