A parametric equation is very similar to a function: it consists of some numbers in a specified set, called parameters or independent variables, which determine the result of the dependent variable. For example, kinematics, the parameter is usually "time", and the result of the equation is speed, position and so on.

Usage:

The parameter equation of a circle x = a+r cos θ y = b+r sin θ (θ∈ [0,2π)) (a, b) is the center coordinate, r is the radius of the circle, θ is the parameter, and (x, y) is the coordinate passing through the point.

The parametric equation of ellipse x = a cos θ y = b sin θ (θ∈ [0,2π]) a is the length of the major axis b, and the length of the minor axis θ is the parameter.

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The parametric equation of hyperbola x=a secθ (secθ) y=b tanθ a is the real semi-axis length b and the imaginary semi-axis length θ is the parameter.

The parametric equation of parabola x = x = 2pt 2y = 2pt p indicates that the distance t from the focus to the directrix is a parameter.

The parameter equation of a straight line x=x'+tcosa y=y'+tsina, x', y' and a represent the straight line passing through (x', y'), the inclination angle is a, and t is the parameter. Or x=x'+ut, y=y'+vt (t∈R)x', y' straight line passes through a fixed point (x', y'), and u and v represent the direction vector d=(u, v) of the straight line.

The involute of the circle x = r (cos φ+φ sin φ) y = r (sin φ-φ cos φ) (φ ∈ [0,2π]) r is the radius φ of the base circle as a parameter.

Use:

1, which can more clearly reflect the relationship between quantity and quantity.

2. It can solve some problems that can't be solved or are difficult without parametric equations.

Hope to adopt