12.1 Parametric Equations Math 6B Calculus II. Parametrizations and Plane Curves  Path traced by a particle moving alone the xy plane. Sometimes the.

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Presentation transcript:

12.1 Parametric Equations Math 6B Calculus II

Parametrizations and Plane Curves  Path traced by a particle moving alone the xy plane. Sometimes the graph cannot be expressed as a function of x or y.

Definition  If x and y are continuous functions x = f (t), y = g(t) over an interval of t – values, then the set of points (x, y) = ( f (t), g(t)) defined by these equations is a curve in the coordinate plane.

Definition  The equations are parametric equations. The variable t is a parameter for the curve and its domain I is the parameter interval. If I is a closed interval,, the pt. ( f (a), g(a)) is the initial point of the curve and ( f (b), g(b)) is called the terminal point of the curve.

Definition  When we give parametric equations and a parameter interval for a curve in the plane, we say that we have parameterized the curve. The equations and interval constitute a parameterization of the curve.

T angents  To find the slope of the tangent dy/dx from the parametric equations x = f (t) and y = g (t), let us use the chain rule of dy/dt

Tangents  We can get dy/dx by itself and therefore get the slope of the tangent line.