Find the eccentricity of an ellipse whose length of the minor axis is equal to half of the length between foci.

Sure, let's solve this step by step.

1. The length of the minor axis of an ellipse is given by 2b, where b is the semi-minor axis.

2. The distance between the foci of an ellipse is given by 2ae, where a is the semi-major axis and e is the eccentricity.

3. According to the problem, 2b = 1/2 * 2ae. Simplifying this, we get b = ae/2.

4. The relationship between a, b, and e in an ellipse is given by the equation a^2 = b^2 + (ae)^2.

5. Substituting b = ae/2 into this equation, we get a^2 = (ae/2)^2 + (ae)^2.

6. Simplifying this, we get a^2 = a^2 * e^2/4 + a^2 * e^2.

7. Dividing through by a^2, we get 1 = e^2/4 + e^2.

8. Simplifying this, we get 1 = 5e^2/4.

9. Solving for e, we get e = sqrt(4/5) = 0.8944.

So, the eccentricity of the ellipse is approximately 0.8944.