# Find the equation of ellipse whose eccentricity is 2/3 , latus rectum is 5 and thecentre is (0, 0).

Equation of an ellipse = , whereas

Length of latus rectum =

Length of minor axis = 2b

b2 = a2 (1 - e2) --------- (i)

Length of Latus Rectum =

b2 = 2.5 a --------- (ii)

[Putting the values in equation (i)]

22.5 a = 5a2

5a2 - 22.5a = 0

5a (a – 4.5) = 0

a = 0 {Not Possible, as the length of latus rectum is 5 units} or 4.5

[Putting the values in equation (ii)]

Equation of an ellipse =

Equation of an ellipse is

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