In coordinate Geometry, the locus of all points in an ellipse which satisfy the equations
⇒ x = s cos (u) and y = t sin (u); where x, and y are the coordinates of any Point on the ellipse, s and t denotes the radius on the x and y axis respectively and ‘u’ denotes the parameter of an ellipse and The Range of an ellipse lies form 0 to 2⊼ radians.
Now we will see the parametric equation of an ellipse. We can say that the equation of an ellipse is almost similar to the equation of a Circle. Now we talk about the difference between an ellipse and a circle. There is only one radius present in a circle and in case of ellipse two radius is present. One radius of an ellipse is measured along to the x – axis and other radius is measured along to the y – axis. It is clearer by the given figure:
In coordinate geometry, if ellipse is centered on the origin (0, 0) then the equation of ellipse is given by:
x = s cos (u) and y = t sin (u); where s is the radius along to the x – axis and ‘t’ is the radius along to the y – axis.
Now we will see, what happen if the center of ellipse is not at origin Position? In this case, we have to add and subtract fixed value to the x and y coordinates. Let ‘f’ and ‘g’ are the coordinates of the center of an ellipse then we have to add ‘f’ and ‘g’ to the x and y coordinates. So the parametric equation as:
⇒ ⇒ x = f + r cos (u) and y = g + r sin (u);
This is all about ellipse parametric equation.