The eccentricity e of an ellipse satisfies the condition.

Options

A. `e lt 0`
B. `0 lt e lt 1`
C. e = 1
D. `e gt 1`

Answer

To solve the question regarding the eccentricity \( e \) of an ellipse, we need to understand the definition and properties of eccentricity in conic sections.

### Step-by-Step Solution:

1. **Understanding Eccentricity**:
Eccentricity is a measure of how much a conic section deviates from being circular. It is defined as the ratio of the distance from a point on the conic section to a focus and the distance from that point to the nearest directrix.

2. **Eccentricity Values**:
- For a **circle**, the eccentricity \( e = 0 \).
- For an **ellipse**, the eccentricity \( e \) is between 0 and 1 (i.e., \( 0 < e < 1 \)).
- For a **parabola**, the eccentricity \( e = 1 \).
- For a **hyperbola**, the eccentricity \( e > 1 \).

3. **Condition for Ellipse**:
Given the condition that the eccentricity \( e \) of an ellipse satisfies a specific range, we conclude that:
\[ 0 < e < 1 \]

4. **Conclusion**:
Therefore, the eccentricity of an ellipse is always between 0 and 1. This means that if the question provides options, the correct answer would be the one that states \( e \) is between 0 and 1.

### Final Answer:
The eccentricity \( e \) of an ellipse satisfies the condition \( 0 < e < 1 \).

---