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 uniquely 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 (t ∈ ℝ) are parametric equations for the parabola y² = 4ax; and x = acosθ‎, y = bsinθ‎ (θ‎ ∈ [0, 2π‎)) are parametric equations for the ellipse

The gradient dy/dx of the curve at any point can be found, if x′(t) ≠ 0, from dy/dx=y′(t)/x′(t).