The parameter equation of a circle with the center at the origin and radius =R is: x=Rcost, y=Rsint.
The parametric equation of the garden with (a, b) as the center and radius =R: x=a+Rcost, y=b+Rsint.
The equation of sphere in space R is a parametric equation. If the center of the circle is (a, b, c) and the radius is r, it is expressed as: (x-a)2+(y-b)2+(z-c)2=R2.
It can also be expressed as a parametric equation with u and v as parameters: x = a+rcosuy = b+rsinusosvz = c+rsinusinv (0 ≤θ≤ 2π, 0≤φ≤π).
definition
Generally speaking, in the plane rectangular coordinate system, if the coordinates x and y of any point on the curve are all functions of a variable t, and for each allowable value of t, the points (x, y) determined by the equations are all 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.