Calculus › Section K · Conics, parametric equations, and polar coordinates › Topic K.1
Conic sections and calculus
Slice a cone at different angles and you get the circle, parabola, ellipse and hyperbola. These four curves carry orbits, telescope mirrors and navigation systems, and their equations come from a single idea about distance.
In this topic
- Four curves from one cone
- The parabola: focus and directrix
- Worked example: focus and directrix
- The ellipse: a constant sum
- Worked example: analysing an ellipse
- The hyperbola: a constant difference
- Worked example: analysing a hyperbola
- Eccentricity: one number for every conic
- Tangent lines and reflection
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP