Algebra › Section K · Conics › Topic K.3
Ellipses
An ellipse is the oval of the conic family — the shape you get slicing a cone on a tilt, or looping a string around two pins. Its algebra is a study in two denominators: the larger one always belongs to the major axis, and the foci hide a Pythagorean relation underneath.
In this topic
- Two pins and a string
- Anatomy: major, minor, and the foci
- Standard form at the origin
- Worked example: from equation to graph
- When the major axis is vertical
- Centre not at the origin
- Worked example: a whispering gallery
- Common mistakes to avoid
- Key takeaways
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