a, b = 1, 2
phi = np.linspace(3, 10, 100)
x1 = a*phi - b*np.sin(phi)
y1 = a - b*np.cos(phi)

x2=phi
y2=np.sin(phi)+2
x,y=intersection(x1,y1,x2,y2)

plt.plot(x1,y1,c="r")
plt.plot(x2,y2,c="g")
plt.plot(x,y,"*k")
plt.show()