Question

The length of the semi-latus rectum of an ellipse is one third of its major axis, its eccentricity would be

• A. (2)/(3)
• B. √((2)/(3))
• C. \dfrac1√(3)
• D. \dfrac1√(2)

Hint:

For ellipses, always relate parameters using: e²=1-(b²)/(a²)

Answer 1

The Correct Option is B

Step 1: For an ellipse: Semi-latus rectum l=(b²)/(a) Step 2: Given major axis =2a, so: l=(1)/(3)(2a)=(2a)/(3) Step 3: Hence, (b²)/(a)=(2a)/(3) ⟹ (b²)/(a²)=(2)/(3) Step 4: Eccentricity: e²=1-(b²)/(a²)=1-(2)/(3)=(1)/(3)× 2=(2)/(3) ⟹ e=√((2)/(3))