Q. 164.0( 2 Votes )

Find the eq

Answer :

Given that we need to find the equation of the ellipse whose distance between the foci is 8 units and distance between the directrices is 18 units.



We know that the distance between the foci is 2ae.


2ae = 8


ae = 4 ..... - (1)


We know that the distance between the directrices is .



..... - (2)


(1)×(2)



a2 = 36 .... (3)


a = 6


We know that eccentricity of an ellipse is



36 - b2 = 16


b2 = 20 ..... (4)


The equation of the ellipse is,




5x2 + 9y2 = 180


The equation of the ellipse is 5x2 + 9y2 = 180.


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