SUMMARY
In the context of the ellipse equation \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), when \(b > a\), the y-axis serves as the major axis. This is because the major axis is defined as the longest diameter of the ellipse, which corresponds to the maximum value between \(a\) and \(b\). Thus, the distance \(r\) from the center to any point on the ellipse is constrained by the values of \(a\) and \(b\), confirming that the major axis is always represented by the larger of the two values.
PREREQUISITES
- Understanding of ellipse equations and their standard forms
- Familiarity with the concepts of major and minor axes
- Basic knowledge of coordinate geometry
- Ability to interpret mathematical inequalities
NEXT STEPS
- Study the properties of ellipses in conic sections
- Learn about the geometric interpretations of major and minor axes
- Explore the derivation of the ellipse equation from its definition
- Investigate the applications of ellipses in physics and engineering
USEFUL FOR
Students of mathematics, educators teaching geometry, and anyone interested in the properties of conic sections will benefit from this discussion.