Ellipse

python code

   import numpy as np
   from matplotlib import pyplot as plt
   from math import pi, cos, sin
   u=1.       #x-position of the center
   v=0.5      #y-position of the center
   a=2.       #radius on the x-axis
   b=1.5      #radius on the y-axis
   t_rot=pi/4 #rotation angle

   t = np.linspace(0, 2*pi, 100)
   Ell = np.array([a*np.cos(t) , b*np.sin(t)])  
        #u,v removed to keep the same center location
   R_rot = np.array([[cos(t_rot) , -sin(t_rot)],[sin(t_rot) , cos(t_rot)]])  
        #2-D rotation matrix

   Ell_rot = np.zeros((2,Ell.shape[1]))
   for i in range(Ell.shape[1]):
       Ell_rot[:,i] = np.dot(R_rot,Ell[:,i])

   plt.plot( u+Ell[0,:] , v+Ell[1,:] )     #initial ellipse
   plt.plot( u+Ell_rot[0,:] , v+Ell_rot[1,:],'darkorange' )    #rotated ellipse
   plt.grid(color='lightgray',linestyle='--')
   plt.show()