Parametric equations and parametric coordinates of an ellipse

The circle described on the major axis of an ellipse as diameter is called an auxiliary circle of the ellipse.

For the ellipse x²/a² + y²/b² = 1
Auxiliary circle is x² + y² = a²

Parametric coordinates of ellipse

If ф is the angle made by the line joining centre of ellipse with a point (x,y) on the ellipse x = a cos ф and y = b sin ф are the parametric coordinates of the ellipse x²/a² + y²/b² = 1, a>b