When does the ellipse become a circle ?

Answer

To determine when an ellipse becomes a circle, we can analyze the properties of both shapes. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- An **ellipse** is defined by its major axis (length 2b) and minor axis (length 2a).
- A **circle** is a special case of an ellipse where the lengths of the major and minor axes are equal.

2. **Setting Up the Axes**:
- Let the length of the major axis be denoted as \(2b\).
- Let the length of the minor axis be denoted as \(2a\).

3. **Condition for a Circle**:
- For an ellipse to become a circle, the lengths of the major and minor axes must be equal. Thus, we set the condition:
\[ 2a = 2b \]

4. **Simplifying the Condition**:
- Dividing both sides of the equation by 2 gives us:
\[ a = b \]

5. **Conclusion**:
- Therefore, an ellipse becomes a circle when the lengths of the semi-major axis and the semi-minor axis are equal, which means \(a = b\).

### Final Answer:
An ellipse becomes a circle when the lengths of the semi-major axis and semi-minor axis are equal, i.e., \(a = b\).

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