Parametric equation, a mathematical term, is very similar to function. They are all numbers in a specific set, called parameters or independent variables, to 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.
Generally speaking, in the plane rectangular coordinate system, if the coordinates x and y of any point on the curve are functions of a variable t, and for each allowable value of t, the points (x, y) determined by the equations are on this curve, then this equation is called the parametric equation of the curve, and the variable t connecting the variables x and y is called the parametric variable, which is called the parameter for short. Relatively speaking, the equation that directly gives the point coordinate relationship is called the constant equation.
Example of parametric equation
The polar coordinate parameter equation of the curve ρ=f(t), θ=g(t).
The parameter equation of a circle x=a+rcosθ, y = b+rsin θ (θ∈ [0 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=acosθ, y = bsin θ (θ ∈ [0 0,2π]) A is the length of the major semi-axis, B is the length of the minor semi-axis, and θ is the parameter.
The parametric equation of hyperbola is x=asecθ (secant) and y=btanθ, where a is the real semi-axis length, b is the imaginary semi-axis length, and θ is the parameter.
The parametric equation of parabola is x = 2pt 2, y=2pt, p represents the distance from the focus to the directrix, and t is the parameter.
The parametric equation of a straight line x=x'+tcosa, y=y'+tsina, x', y' and a represents a straight line passing through (x', y'), with an inclination angle of a and a parameter of t.
Refer to the above content: Baidu Encyclopedia-Parameter Equation