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Polar equation

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College Algebra

Definition

A polar equation is a mathematical expression that defines a relationship between the radius $r$ and the angle $\theta$ of a point in the polar coordinate system. It is commonly used to describe conic sections and other geometric shapes.

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5 Must Know Facts For Your Next Test

  1. Polar equations use $r$ (radius) and $\theta$ (angle) instead of $x$ and $y$ coordinates.
  2. Common forms of polar equations for conic sections include $r = \frac{ed}{1 + e \cos(\theta)}$ for ellipses, hyperbolas, and parabolas.
  3. The eccentricity $e$ determines the type of conic section: ellipse $(0 < e < 1)$, parabola $(e = 1)$, or hyperbola $(e > 1)$.
  4. Converting between Cartesian and polar coordinates involves the formulas: $x = r \cos(\theta)$ and $y = r \sin(\theta)$.
  5. Graphs of polar equations can exhibit symmetry about the pole (origin), the line $\theta = \frac{\pi}{2}$, or the polar axis.

Review Questions

  • What is the general form of a polar equation for an ellipse?
  • How do you convert from Cartesian coordinates to polar coordinates?
  • What does the eccentricity value indicate about a conic section in a polar equation?
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