How to plot multiple parametric plots in a single figure?

I need to plot a family of parametric curves in a single figure for each alpha values as mentioned in the code

import numpy as np
from sympy import *  
from sympy.plotting import plot_parametric
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D


a=45
t = symbols('t')
for alpha in np.arange(0.5,3,.1):
    M=a*sqrt(cos(2*t)+sqrt(pow(alpha,4)+pow(sin(2*t),2)))
    x = M*cos(t)
    y = M*sin(t)
    plot_parametric(x, y, (t, 0, 2*pi))

The code returns a sequence of 2D plots for each alpha value. Instead, I want to plot the whole set of plots in one figure, something like this image attached

Any solution?

from numpy import arange, cos, linspace, pi, sin, sqrt
from matplotlib.pyplot import colorbar, Normalize, show, subplots
from matplotlib.cm import ScalarMappable, viridis

a=45
t= linspace(0, 2*pi, 2001)

norm = Normalize(vmin=0.5, vmax=3)
cmap = viridis
sm = ScalarMappable(cmap=cmap, norm=norm)

fig, (ax_xy, ax_tM) = subplots(1, 2, figsize=(10, 4), constrained_layout=1)

for alpha in arange(0.5,3,.1):
    color = cmap(norm(alpha))
    M=a*sqrt(cos(2*t)+sqrt(pow(alpha,4)+pow(sin(2*t),2)))
    x = M*cos(t)
    y = M*sin(t)
    ax_tM.plot(t, M, color=color)
    ax_xy.plot(x, y, color=color)
colorbar(sm, aspect=40)
show()