title: Drawing elliptical orbit in Python (using numpy, matplotlib)
body: <p>I wonder how can I draw elliptical orbit by using the equation ay<sup>2</sup> + bxy + cx + dy + e = x<sup>2</sup> ?</p>
  
  <p>I have first determined the a,b,c,d,e constants and now I assume by giving x values I will obtain y and this will give me the graph I want but I couldn't do it by using matplotlib.</p>
  
  <p>I would really appreciate, if you could help me! </p>
  
  <p>EDIT: I added the code here.</p>
  
  <pre><code>from numpy import linalg
  from numpy import linspace
  import numpy as np
  from numpy import meshgrid
  import random
  import matplotlib.pyplot as plt
  from scipy import optimize
  
  x = [1.02, 0.95, 0.87, 0.77, 0.67, 0.56, 0.44, 0.30, 0.16, 0.01]
  y = [0.39, 0.32, 0.27, 0.22, 0.18, 0.15, 0.13, 0.12, 0.12, 0.15]
  
  my_list = [] #It is the main list.
  b = [0] * len(x) # That is the list that contains the results that are given as x^2 from the equation.
  
  def fxn():  # That is the function that solves the given equation to find each parameter.
      global my_list
      global b
      for z in range(len(x)):
          w = [0] * 5
          w[0] = y[z] ** 2
          w[1] = x[z] * y[z]
          w[2] = x[z]
          w[3] = y[z]
          w[4] = 1
          my_list.append(w)
          b[z] = x[z] ** 2
  
      t = linalg.lstsq(my_list, b)[0]
      print 'List of list representation is', my_list
      print 'x^2, the result of the given equation is', b
      print '\nThe list that contains the parameters is', t
  
  fxn()
  t = linalg.lstsq(my_list, b)[0]
  
  print '\nThe constant a is', t[0]
  print 'The constant b is', t[1]
  print 'The constant c is', t[2]
  print 'The constant d is', t[3]
  print 'The constant e is', t[4]
  </code></pre>
  
  <p>EDIT: Here are the constant values:</p>
  
  <pre><code>a = -4.10267300566
  b = 1.10642410023
  c = 0.39735696603
  d = 3.05101004127
  e = -0.370426134994
  </code></pre>