Calculus › Section K · Conics, parametric equations, and polar coordinates › Topic K.3
Calculus with parametric equations
Once a curve is written parametrically, the whole calculus toolkit comes along: slopes and tangent lines from a ratio of two derivatives, plus arc length and surface area formulas that adapt naturally to motion.
In this topic
- Slope without eliminating the parameter
- Worked example: a tangent line
- Horizontal and vertical tangents
- The second derivative
- Arc length of a parametric curve
- Worked example: quarter circle length
- Surfaces of revolution, parametric form
- Worked example: the surface of a sphere
- Common mistakes to avoid
- Key takeaways
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Standards: 9 (BC)