This interactive graph illustrates the key components of an ellipse based on the standard equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. You can adjust the semi-major/minor axes 'a' and 'b' using the sliders below the graph.
- Center: The midpoint of the ellipse, located at $(0,0)$.
- Foci: Two fixed points inside the ellipse. The sum of the distances from any point on the ellipse to the two foci is constant.
- Vertices: The points on the ellipse that intersect the major axis.
- Covertices: The points on the ellipse that intersect the minor axis.
- Major Axis: The longest diameter of the ellipse, passing through the foci and vertices. Its length is $2 \times \max(a, b)$.
- Minor Axis: The shortest diameter of the ellipse, perpendicular to the major axis and passing through the center. Its length is $2 \times \min(a, b)$.
- Latera Recta: Chords perpendicular to the major axis passing through the foci.
- Directrices: Two lines perpendicular to the major axis, related to the foci and eccentricity of the ellipse.