import numpy as np
import matplotlib.pyplot as plt

fig = plt.figure()
axis = fig.add_subplot(1,1,1)

x, y = np.mgrid[-2: 2: 4001j, -2: 2: 4001j]

axis.set_title('Ellipse')
axis.set_xlabel(r'$x$', fontsize=20, fontname='serif')
axis.set_ylabel(r'$y$', fontsize=20, fontname='serif')
axis.tick_params(axis='both', length=10, which='major')
axis.tick_params(axis='both', length=5,  which='minor')
axis.minorticks_on()
axis.set_aspect('equal', 'box')
axis.set(xlim=(-2, 2), ylim=(-2, 2))

axis.contour(x, y, x**2 - 2*x*y + 2*y**2, [1])

plt.show()
fig.savefig('plot.svg', transparent=False)