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Expressions & functions10 / 68

Parametric & polar curves

Parametric curves describe x and y together. Polar curves describe distance from the origin at an angle.

Find it

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Parametric and polar expressions with their parameter intervals.
Parametric and polar expressions with their parameter intervals.Click to enlarge ↗

Try it step by step

  1. For a parametric curve, enter a pair whose coordinates depend on t.
  2. For a polar curve, write r as a function of .
  3. Set the curve’s parameter interval. Use Radians or Degrees consistently.
  4. Select the curve and open Trace to follow t or instead of an ordinary x input.

Examples to try

Each card is one input. For definitions, enter the cards in order. Formula-only cards belong in the tool described above.

An ellipse for .

A polar curve for in radians.

Options explained

Coordinate pair
The first formula determines x, the second y. The shared parameter is t.
Polar radius
The radius may be negative; the plotted point follows the usual polar-coordinate interpretation.
Parameter range
Minimum and maximum control which part of the curve is drawn. The renderer samples it automatically.
Polar grid
Graph settings can show radius rings and angle rays; choosing that grid does not convert existing equations.
Analysis
Trace and curve intersections support these curves. Canvas tangent/area previews use their own parameter fields.

Screenshot

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