Question

Find the eccentricity of an ellipse whose latus rectum is one half of its major axis?

Answer 1

major axis = 2 * a
ellipse :   x²/a² + y²/b² = 1
e² = (a² - b²)/a²  - equation 1
latus rectum = chord perpendicular to major axis at a focus = 2 l = 2 b² / a
2 b²/a = 1/2 * 2a  => 2 b² = a²        =>  b² = a²/2
so  e² = 1/2  substituting value of b²  from equation 1
 e = 1/√2

Answer 2

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