Q. 125.0( 1 Vote )

Find the equation of an ellipse whose eccentricity is 2/3, the latus - rectum is 5 and the centre is at the origin.

Answer :

Given that we need to find the equation of the ellipse whose eccentricity is , latus - rectum is 5 and centre is at origin.



Let us assume the equation of the ellipse is - - - - (1) (a2>b2) since centre is at origin.


We know that eccentricity of the ellipse is




9(a2 - b2) = 4a2


5a2 = 9b2


..... - - - (2)


We know that length of the latus - rectum is







From (2),




The equation of the ellipse is





20x2 + 36y2 = 405


The equation of the ellipse is 20x2 + 36y2 = 405.


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