'A parameterized point on the ellipse.
Parameters
parameter : str, optional
Default value is \'t\'.
Returns
arbitrary_point : Point
Raises
ValueError
When `parameter` already appears in the functions.
See Also
sympy.geometry.point.Point
Examples
>>> from sympy import Point, Ellipse
>>> e1 = Ellipse(Point(0, 0), 3, 2)
>>> e1.arbitrary_point()
Point2D(3*cos(t), 2*sin(t))'

def arbitrary_point(self, parameter='t'):

    t = _symbol(parameter)
    if (t.name in (f.name for f in self.free_symbols)):
        raise ValueError(filldedent(('Symbol    %s    already    appears    in    object    and    cannot    be    used    as    a    parameter.' % t.name)))
    return Point((self.center.x + (self.hradius * cos(t))), (self.center.y + (self.vradius * sin(t))))
