from sympy import *
_x = symbols('x')
_y = symbols('y')
class circle:
    def __init__(self,x,y,r):
        self.x = x
        self.y = y
        self.r = r

    def get_expr(self):
        return self.r**2 - (pow(_x-self.x,2) + pow(_y-self.y,2))

    def get_x(self,y):
        expr = self.get_expr()
        expr = expr.subs(_y,y)
        return solve(expr,_x)

    def get_y(self,x):
        expr = self.get_expr()
        expr = expr.subs(_x,x)
        return solve(expr,_y)

    def get_diff(self,dydx=True):
        expr = self.get_expr()
        if dydx:
            return expr.diff(_x)
        else:
            return expr.diff(_y)
if __name__ == "__main__":
    unit_circle = circle(0,0,1)