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parametrization


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(of a curve)

A method of associating, with every value of a parameter t in some interval I (or some other subset of R), a point P(t) on the curve such that every point of the curve corresponds to some value of t. Often this is done by giving the x- and y-coordinates of P as functions of t, so that the coordinates of P may be written (x(t), y(t). The equations that give x and y as functions of t are parametric equations for the curve. For example, x=at2, y=2at (tR) are parametric equations for the parabola y2=4ax; and x=a cos θ, y=b sin θ (θ ∈ [0, 2π) are parametric equations for the ellipseThe gradient dy/dx of the curve at any point can be found, if x′(t) ≠ 0, from dy/dx=y′(t)/x′(t).

Subjects: Mathematics.


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