Patches animation in matplotlib

I'm trying to create a simple particle animation using matplotlib, like this:

import numpy as np
from matplotlib import pyplot as plt
from matplotlib import animation

fig = plt.figure()
fig.set_dpi(100)
fig.set_size_inches(7, 6.5)

ax = plt.axes(xlim=(0, 10), ylim=(0, 10))
patch = plt.Circle((5, -5), 0.75, fc='y')

def init():
    patch.center = (5, 5)
    ax.add_patch(patch)
    return patch,

def animate(i):
    x, y = patch.center
    x = 5 + 3 * np.sin(np.radians(i))
    y = 5 + 3 * np.cos(np.radians(i))
    patch.center = (x, y)
    return patch,

anim = animation.FuncAnimation(fig, animate, 
                               init_func=init, 
                               frames=36, 
                               interval=20,
                               blit=True)

HTML(anim.to_jshtml())

Now, I want to wrap the plt.Circle object in a "Particle" class, so that I can add other functionality (like giving it a velocity and so on). This is what I tried:

import numpy as np
from matplotlib import pyplot as plt
from matplotlib import animation

fig = plt.figure()
fig.set_dpi(100)
fig.set_size_inches(7, 6.5)

ax = plt.axes(xlim=(0, 10), ylim=(0, 10))

class Particle:
    def __init__(self,x,y):
        self.x = x
        self.y = y
    def show(self):
        return plt.Circle((self.x, self.y), 0.75, fc='y')

p = Particle(5, -5)

def init():
    ax.add_patch(p.show())
    return p.show(),

def animate(i):
    p.x = 5 + 3 * np.sin(np.radians(i))
    p.y = 5 + 3 * np.cos(np.radians(i))
    return p.show(),

anim = animation.FuncAnimation(fig, animate, 
                               init_func=init, 
                               frames=36, 
                               interval=20,
                               blit=True)

HTML(anim.to_jshtml())

why doesn't this work?

I expected this to behave the same way as the first code, since p.show() returns a plt.Circle object.

You should update the position of an existing Circle object.

import numpy as np
from matplotlib import pyplot as plt
from matplotlib import animation
from IPython.display import HTML

fig = plt.figure()
fig.set_dpi(100)
fig.set_size_inches(7, 6.5)

ax = plt.axes(xlim=(0, 10), ylim=(0, 10))

class Particle:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        self.circle = plt.Circle((self.x, self.y), 0.75, fc='y')

    def show(self):
        self.circle.set_center((self.x, self.y))
        return self.circle

p = Particle(5, 5)
ax.add_patch(p.show())

def init():
    p.show()
    return p.show(),

def animate(i):
    p.x = 5 + 3 * np.sin(np.radians(i * 10))
    p.y = 5 + 3 * np.cos(np.radians(i * 10))
    p.show()
    return p.show(),

anim = animation.FuncAnimation(fig, animate, 
                               init_func=init, 
                               frames=36, 
                               interval=100,
                               blit=True)

HTML(anim.to_jshtml())