13.
What is the standard equation of an ellipse centered at the origin with axes aligned along the coordinate axes?

a.

b.

c.

d.

The standard equation of an ellipse centered at the origin \((0,0)\) with axes aligned along the coordinate axes is:  

\[
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
\]

where:  
- \(a\) is the **semi-major axis** (the larger value between \(a\) and \(b\)),  
- \(b\) is the **semi-minor axis**,  
- If \(a > b\), the ellipse is **horizontal**; if \(b > a\), it is **vertical**.

Would you like details on how this equation is derived?  

### Related Questions:
1. What is the difference between an ellipse and a circle in terms of equations?
2. How do you determine the foci of an ellipse?
3. What happens if \( a = b \) in the equation of an ellipse?
4. How do you find the eccentricity of an ellipse?
5. What are the parametric equations of an ellipse?

**Tip:** The sum of the distances from any point on the ellipse to the two foci is always constant!

What is the standard equation of an ellipse centered at the origin with axes aligned along the coordinate axes?

Discover the standard equation of an ellipse centered at the origin with axes aligned along the coordinate axes. The equation \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) explains the relationship between the semi-major and semi-minor axes. Learn key properties of ellipses, including how the ellipse orientation changes based on the values of \(a\) and \(b\). Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation