Parametric Equations

What Are Parametric Equations? 🕰️

**Parametric equations** define a curve by expressing its coordinates ($x$ and $y$) as functions of a single independent variable, called a **parameter** (usually $t$).

Instead of writing $y = f(x)$, we have a pair of equations:

$x = x(t)$
$y = y(t)$

Think of the parameter $t$ as **time**. As $t$ changes, the point $(x,y)$ moves along a path. This is useful for describing the motion of an object.

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Video: Visualizing a Parametric Curve 🎬

Watch this video to see how a point moves along a path as the parameter changes.

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Practice Problems

Convert the given parametric equations to a single Cartesian equation by eliminating the parameter.

1) $x = t+2, y = t^2+1$

2) $x = \cos\theta, y = \sin\theta$

3) $x = 3\cos t, y = 2\sin t$

4) $x=2t-1, y=3t+4$

⚡ Parametric Quiz

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