Chapter 10 Conics, Parametric Equations, and Polar Coordinates

Chapter 10

Conics, Parametric Equations, and Polar

Coordinates

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Figure 10.1 and Figure 10.2


Theorem 10.1 Standard Equation of a Parabola


Theorem 10.2 Reflective Property of a Parabola and Figure 10.6




Theorem 10.3 Standard Equation of an Ellipse


Theorem 10.4 Reflective Property of an Ellipse


Definition of Eccentricity of an Ellipse and Figure 10.12


Theorem 10.5 Standard Equation of a Hyperbola


Theorem 10.6 Asymptotes of a Hyperbola and Figure 10.15


Definition of Eccentricity of a Hyperbola and Figure 10.17


Definition of a Plane Curve


Definition of a Smooth Curve


Figure 10.26




Theorem 10.7 Parametric Form of the Derivative


Theorem 10.8 Arc Length in Parametric Form


Theorem 10.9 Area of a Surface of Revolution


Figure 10.36


Figure 10.37


Figure 10.38


Theorem 10.10 Coordinate Conversion


Theorem 10.11 Slope in Polar Form


Theorem 10.12 Tangent Lines at the Pole and Figure 10.48


Limacons


Rose Curves


Circles and Lemniscates


Figure 10.49


Figure 10.50


Theorem 10.13 Area in Polar Coordinates




Theorem 10.14 Arc Length of a Polar Curve


Theorem 10.15 Area of a Surface of Revolution


Theorem 10.16 Classification of Conics by Eccentricity and Figure 10.58


Theorem 10.17 and Figure 10.60

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Chapter 10 Conics, Parametric Equations, and Polar Coordinates