11.2 Polar Equations and Graphs

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11.2Polar Equations and Graphs
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An equation whose variables are polar coordinates
is called a polar equation. The graph of a polar
equation consists of all points whose polar
coordinates satisfy the equation.
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Identify and graph the equation r 2
Circle with center at the pole and radius 2.
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Theorem
Let a be a nonzero real number, the graph of the
equation
is a horizontal line a units above the pole if a
gt 0 and a units below the pole if a lt 0.
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Theorem
Let a be a nonzero real number, the graph of the
equation
is a vertical line a units to the right of the
pole if a gt 0 and a units to the left of the
pole if a lt 0.
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Theorem
Let a be a positive real number. Then,
Circle radius a center at (0, a) in rectangular
coordinates.
Circle radius a center at (0, -a) in
rectangular coordinates.
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Theorem
Let a be a positive real number. Then,
Circle radius a center at (a, 0) in rectangular
coordinates.
Circle radius a center at (-a, 0) in
rectangular coordinates.
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Theorem Tests for Symmetry
Symmetry with Respect to the Polar Axis (x-axis)
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Theorem Tests for Symmetry
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Theorem Tests for Symmetry
Symmetry with Respect to the Pole (Origin)
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The tests for symmetry just presented are
sufficient conditions for symmetry, but not
necessary.
In class, an instructor might say a student will
pass provided he/she has perfect attendance.
Thus, perfect attendance is sufficient for
passing, but not necessary.
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Symmetry
Polar axis
Symmetric with respect to the polar axis.