If the distance between the foci of an ellipse is equal to the length of the latus - rectum, write the eccentricity of the ellipse.
Given that we need to find the eccentricity of the ellipse whose latus - rectum is equal to the distance between the foci.
We know that length of latus rectum is and distance between foci is 2ae.
⇒
⇒ b2 = a2e.
We know that eccentricity of the ellipse is b2 = a2(1 - e2)
⇒ a2(1 - e2) = a2e
⇒ e2 + e - 1 = 0
⇒
⇒ (since e>0)