Find the length of major axis, minor axis, latus rectum, eccentricity of the ellipse of
x^2 + y^2 = 16

The given equation is \( x^2 + y^2 = 16 \). 

This is the equation of a circle, not an ellipse. The equation of a circle is generally written as:
\[
x^2 + y^2 = r^2
\]
where \( r \) is the radius of the circle.

### Characteristics of the Circle:
- **Radius**: \( r = \sqrt{16} = 4 \).
- **Length of Major Axis**: Since it's a circle, the major axis is the diameter, which is \( 2r = 8 \).
- **Length of Minor Axis**: The minor axis is also the diameter, so \( 2r = 8 \).
- **Latus Rectum**: The concept of latus rectum applies to ellipses, not circles. For circles, every chord that passes through the center is of equal length (equal to the diameter).
- **Eccentricity**: The eccentricity \( e \) of a circle is 0, as all points on the circle are equidistant from the center.

Thus, the given equation represents a circle with the following characteristics:
1. **Length of Major Axis**: 8 units
2. **Length of Minor Axis**: 8 units
3. **Latus Rectum**: Not applicable for a circle.
4. **Eccentricity**: 0

Would you like further details or explanations? Here are 5 related questions for deeper understanding:

1. How does the equation of a circle differ from that of an ellipse?
2. What is the geometric significance of eccentricity in an ellipse?
3. How do you derive the equation of a circle from its geometric definition?
4. Can the equation of a circle be considered a special case of an ellipse?
5. How would you find the area of the circle from the given equation?

**Tip:** The eccentricity of a circle is always 0, while for ellipses, it's between 0 and 1.

Find the length of major axis, minor axis, latus rectum, eccentricity of the ellipse of x^2 + y^2 = 16

Explore the geometric properties of the circle given by the equation x^2 + y^2 = 16. Learn about the radius, major axis, minor axis, and eccentricity, with a step-by-step explanation. Suitable for students in Grades 9-11.

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