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x=5cos(t)*cos (at)
y= 5cos(t) + sin(at)
Parametric Equation
A parametric equation describes a 3D structure by defining its x, y, and z coordinates using one or more parameters. These parameters typically represent angles (theta, phi) or distances (u, v) that control how the shape is traced out in 3D space.

Think of it like a recipe for a 3D shape. The equations act as the instructions, and the parameters are the ingredients. By changing the values of the parameters, you can explore different parts of the 3D structure or even generate entirely different shapes from the same basic formula.

Here are some common examples:

*Sphere:* Imagine a sphere being drawn by a point on a string going around a fixed center. The radius of the string is a constant, and the angle traced out by the point corresponds to the parameters (theta, phi) for spherical coordinates.

*Torus:* A torus (donut shape) can be created by using two parameters to define rotations along two different axes. One parameter controls the minor radius, like the thickness of the donut, and the other controls the major radius, the overall size of the torus.

Parametric equations are powerful because they allow you to represent complex 3D shapes with relatively simple formulas. They are widely used in computer graphics, animation, and 3D modeling for creating and manipulating intricate objects.

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