The angle in the elliptic parameter equation corresponds to the angle between the connecting line between the point and the endpoint and the X axis (or Y axis), and only when the center coincides with the origin is the angle from the origin to the point.

Parametric equation, as a mathematical term, is similar to a function: all numbers in a specified set, called parameters or independent variables, 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.

Extended data:

Proof of elliptic parameter equation;

Let the two foci of an ellipse be F 1 and F2 respectively, and the distance between them is 2c. The sum of the distances from any point on the ellipse to F 1 and F2 is 2a (2a >: 2c).

Taking the straight line of F 1 and F2 as the X axis and the vertical line of the line segment F 1F2 as the Y axis, and establishing the rectangular coordinate system xOy, the coordinates of F 1 and F2 are (-c, 0) and (c, 0) respectively.

The parameter equation is:

A is the length of the long semi-axis, b is the length of the short semi-axis, and c is half the focal length; R is the distance from the point P(x, y) on the ellipse to the focus (c, 0), θ is the angle between the line connecting the point P(x, y) on the ellipse and the focus (c, 0) and the Y axis, and Ф is the angle between the line connecting the point P(x, y) on the ellipse and the focus (-c, 0) and the X axis.

References:

Baidu Encyclopedia-Parameter Equation of Ellipse

References:

Baidu encyclopedia-parameter equation