class_docstr: Represents an implicit region in space.
  
  Examples
  ========
  
  >>> from sympy import Eq
  >>> from sympy.abc import x, y, z, t
  >>> from sympy.vector import ImplicitRegion
  
  >>> ImplicitRegion((x, y), x**2 + y**2 - 4)
  ImplicitRegion((x, y), x**2 + y**2 - 4)
  >>> ImplicitRegion((x, y), Eq(y*x, 1))
  ImplicitRegion((x, y), x*y - 1)
  
  >>> parabola = ImplicitRegion((x, y), y**2 - 4*x)
  >>> parabola.degree
  2
  >>> parabola.equation
  -4*x + y**2
  >>> parabola.rational_parametrization(t)
  (4/t**2, 4/t)
  
  >>> r = ImplicitRegion((x, y, z), Eq(z, x**2 + y**2))
  >>> r.variables
  (x, y, z)
  >>> r.singular_points()
  EmptySet
  >>> r.regular_point()
  (-10, -10, 200)
  
  Parameters
  ==========
  
  variables : tuple to map variables in implicit equation to base scalars.
  
  equation : An expression or Eq denoting the implicit equation of the region.
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code: def _regular_point_parabola(self, a, b, c, d, e, f):
      ok = (
          (a, d) != (0, 0)
          and (c, e) != (0, 0)
          and b**2 == 4 * a * c
          and (a, c) != (0, 0)
      )
  
      if not ok:
          raise ValueError("Rational Point on the conic does not exist")
  
      if a != 0:
          d_dash, f_dash = (4 * a * e - 2 * b * d, 4 * a * f - d**2)
          if d_dash != 0:
              y_reg = -f_dash / d_dash
              x_reg = -(d + b * y_reg) / (2 * a)
          else:
              ok = False
      elif c != 0:
          d_dash, f_dash = (4 * c * d - 2 * b * e, 4 * c * f - e**2)
          if d_dash != 0:
              x_reg = -f_dash / d_dash
              y_reg = -(e + b * x_reg) / (2 * c)
          else:
              ok = False
  
      if ok:
          return x_reg, y_reg
      else:
          raise ValueError("Rational Point on the conic does not exist")
  
imports: from sympy.core.numbers import Rational
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.functions.elementary.complexes import sign
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.polys.polytools import gcd
  from sympy.sets.sets import Complement
  from sympy.core import Basic, Tuple, diff, expand, Eq, Integer
  from sympy.core.sorting import ordered
  from sympy.core.symbol import _symbol
  from sympy.solvers import solveset, nonlinsolve, diophantine
  from sympy.polys import total_degree
  from sympy.geometry import Point
  from sympy.ntheory.factor_ import core
label_desc: Use image node_id 6 for calling the ImplicitRegion obj's underlying member method code with example usage: obj._regular_point_parabola(a, b, c, d, e, f) and returns: x_reg,  y_reg