A line that divides the ellipse into two equal parts in such a way that one part is a reflection of the other part

The line that divides an ellipse into two equal parts, where one part is a reflection of the other, is known as the **axis of symmetry**. An ellipse has **two axes of symmetry**:

1. **Major Axis**: The longest diameter of the ellipse, passing through both foci, and dividing the ellipse into two mirror-image halves.
2. **Minor Axis**: The shortest diameter of the ellipse, perpendicular to the major axis, and also dividing the ellipse into two symmetrical halves.

Each of these axes reflects one half of the ellipse onto the other.

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Here are five related questions:
1. How do you find the length of the major and minor axes in an ellipse?
2. What are the equations of the axes of symmetry for an ellipse centered at the origin?
3. How does the eccentricity of an ellipse affect its shape and symmetry?
4. What is the significance of the foci in the symmetry of an ellipse?
5. How do you rotate an ellipse and determine the new axes?

**Tip**: When dealing with ellipses, always check whether it is centered at the origin or has been shifted to ensure accurate analysis of symmetry and other properties.

A line that divides the ellipse into two equal parts in such a way that one part is a reflection of the other part.

Understand how the major and minor axes divide an ellipse into two symmetrical halves. This guide covers key geometric concepts of ellipses, including the equation of an ellipse and the properties of its axes. Ideal for students in Grades 9-12.

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