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If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is:

a. 0.5
b. 0.75
c. 1.0
d. 1.5

User Psyeugenic
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1 Answer

3 votes

Final answer:

The eccentricity of the ellipse is 0.5.

Step-by-step explanation:

To find the eccentricity of an ellipse given that the distance between the foci is half the length of its latus rectum, we can use the formula for eccentricity: (e) = fla. Let the distance between the foci be 2c and the length of the latus rectum be 2b. We are given that c = b, so the distance between the foci is 2b and e = 2b / (2a), where a is the length of the semi-major axis. Simplifying, we get e = b / a.

Since b is equal to c and c is half the length of the latus rectum, we can substitute c = b = b/2 in the equation for eccentricity. This gives us e = (b/2) / a, which simplifies to e = 1/2. Therefore, the eccentricity of the ellipse is 0.5 (option a).

User Juan Hernandez
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